FORM 6-K

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D. C. 20549

                        Report of Foreign Private Issuer
                      Pursuant to Rule 13a-16 or 15d-16 of
                       the Securities Exchange Act of 1934

                            For the month of May 2004

                     NORDIC AMERICAN TANKER SHIPPING LIMITED
                 (Translation of registrant's name into English)

                                  Canon's Court
                               22 Victoria Street
                                 Hamilton HM 12
                                     Bermuda
                    (Address of principal executive offices)

     Indicate by check mark whether the registrant files or will file annual
reports under cover Form 20-F or Form 40-F.

                           Form 20-F |X| Form 40-F |_|

     Indicate by check mark whether the registrant by furnishing the information
contained in this Form is also thereby furnishing the information to the
commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

                                 Yes |_| No |X|


INFORMATION CONTAINED IN THIS FORM 6-K REPORT

          Attached hereto as Exhibit 1 is a copy of the Notice of Annual General
Meeting of Shareholder of Nordic American Tanker Shipping Limited (the
"Company") Proxy Statement and the accompanying letter to shareholders of the
Company, each dated May 12, 2004, in connection with the Annual General Meeting
of the Company to be held June 10, 2004.

ADDITIONAL INFORMATION

          BP Plc files annual reports on Form 20-F (File No. 1-6262) and
periodic reports on Form 6-K with the Securities and Exchange Commission
pursuant to the Securities Exchange Act of 1934, as amended.


                                   [NATS LOGO]

                                                      May 12, 2004

TO THE SHAREHOLDERS OF
NORDIC AMERICAN TANKER SHIPPING LIMITED

     Enclosed is a Notice of Annual General Meeting of Shareholders ("Notice")
of Nordic American Tanker Shipping Limited (the "Company") which will be held at
the offices of Seward & Kissel LLP, 20th Floor, One Battery Park Plaza, New
York, New York, on June 10, 2004 at 10:30 a.m. (Eastern Daylight Time), and
related materials.

     At this Annual General Meeting (the "Meeting"), the shareholders of the
Company will consider and vote upon proposals:

     1.   To elect a total of five directors to serve until the next Annual
          General Meeting of shareholders ("Proposal One");

     2.   To approve the appointment of Deloitte & Touche as the Company's
          independent auditors for the fiscal year ending December 31, 2004
          ("Proposal Two"); and

     3.   To transact other such business as may properly come before the
          meeting or any adjournment thereof.

     Adoption of Proposals One and Two requires the affirmative vote of a
majority of the holders of the Common Shares present and voting at the Meeting.

     You are cordially invited to attend the Meeting in person. If you attend
the Meeting, you may revoke your proxy and vote your shares in person.

     WHETHER OR NOT YOU PLAN TO ATTEND THE ANNUAL GENERAL MEETING, PLEASE
COMPLETE, DATE, SIGN AND RETURN THE ENCLOSED PROXY IN THE ENCLOSED ENVELOPE,
WHICH DOES NOT REQUIRE POSTAGE IF MAILED IN THE UNITED STATES. THE VOTE OF EVERY
SHAREHOLDER IS IMPORTANT AND YOUR COOPERATION IN RETURNING YOUR EXECUTED PROXY
PROMPTLY WILL BE APPRECIATED.

     ANY SIGNED PROXY RETURNED AND NOT COMPLETED WILL BE VOTED BY MANAGEMENT IN
FAVOR OF ALL PROPOSALS PRESENTED IN THE PROXY STATEMENT.

                                          Very truly yours,

                                          Herbjorn Hansson
                                          Chairman and Chief Executive Officer


                     NORDIC AMERICAN TANKER SHIPPING LIMITED
                NOTICE OF ANNUAL GENERAL MEETING OF SHAREHOLDERS
                                  JUNE 10, 2004

     NOTICE IS HEREBY given that the Annual General Meeting of the shareholders
of Nordic American Tanker Shipping Limited (the "Company") will be held on June
10, 2004, at 10:30 a.m., Eastern Daylight Time, at the office of Seward & Kissel
LLP, 20th Floor, One Battery Park Plaza, New York, New York 10004, for the
following purposes, of which items 1 and 2 are more completely set forth in the
accompanying Proxy Statement:

          1.   To elect a total of five Directors to serve until the next Annual
               General Meeting of the shareholders;

          2.   To approve the appointment of Deloitte & Touche as the Company's
               independent auditors for the fiscal year ending December 31,
               2004;

          3.   To lay before the shareholders the Company's audited financial
               statements for the year ended December 31, 2003; and

          4.   To transact other such business as may properly come before the
               meeting or any adjournment thereof.

     The Board of Directors has fixed the close of business on May 7, 2004, as
the record date for the determination of the shareholders entitled to receive
notice and to vote at the Annual General Meeting or any adjournment or
postponement thereof.

     WHETHER OR NOT YOU PLAN TO ATTEND THE ANNUAL GENERAL MEETING, PLEASE
COMPLETE, DATE, SIGN AND RETURN THE ENCLOSED PROXY IN THE ENCLOSED ENVELOPE,
WHICH DOES NOT REQUIRE POSTAGE IF MAILED IN THE UNITED STATES. THE VOTE OF EVERY
SHAREHOLDER IS IMPORTANT AND YOUR COOPERATION IN RETURNING YOUR EXECUTED PROXY
PROMPTLY WILL BE APPRECIATED. ANY SIGNED PROXY RETURNED AND NOT COMPLETED WILL
BE VOTED BY MANAGEMENT IN FAVOR OF ALL PROPOSALS PRESENTED IN THE PROXY
STATEMENT.

     IF YOU ATTEND THE MEETING, YOU MAY REVOKE YOUR PROXY AND VOTE IN PERSON.

                                    By Order Of The Board Of Directors


                                    Peter Bubenzer
                                    Secretary

May 12, 2004
Hamilton, Bermuda


                     NORDIC AMERICAN TANKER SHIPPING LIMITED
                                  Canon's Court
                               22 Victoria Street
                             Hamilton HM 12, Bermuda

                             ----------------------

                                 PROXY STATEMENT
                                       FOR
                     ANNUAL GENERAL MEETING OF SHAREHOLDERS
                           TO BE HELD ON JUNE 10, 2004

                            ------------------------

                 INFORMATION CONCERNING SOLICITATION AND VOTING

GENERAL
-------

     The enclosed proxy is solicited on behalf of the Board of Directors (the
"Board" or the "Directors") of Nordic American Tanker Shipping Limited, a
Bermuda company (the "Company"), for use at the Annual General Meeting of
Shareholders to be held at the offices of Seward & Kissel LLP, 20th Floor, One
Battery Park Plaza, New York, New York 10004, on June 10, 2004, at 10:30 a.m.,
Eastern Daylight Time, or at any adjournment or postponement thereof (the
"Meeting"), for the purposes set forth herein and in the accompanying Notice of
Annual General Meeting of Shareholders. This Proxy Statement and the
accompanying form of proxy are expected to be mailed to shareholders of the
Company entitled to vote at the General Meeting on or about May 14, 2004.

VOTING RIGHTS AND OUTSTANDING SHARES
------------------------------------

     On May 7, 2004 (the "Record Date"), the Company had outstanding 9,706,606
common shares, par value $0.01 per share ("Common Shares"). Each shareholder of
record at the close of business on the Record Date is entitled to one vote for
each Common Share then held. One or more shareholders representing at least one
third of the total voting rights of the Company present in person or by proxy at
the Meeting shall be a quorum for the purposes of the Meeting. The Common Shares
represented by any proxy in the enclosed form will be voted in accordance with
the instructions given on the proxy if the proxy is properly executed and is
received by the Company prior to the close of voting at the Meeting or any
adjournment or postponement thereof. Any proxies returned without instructions
will be voted for the proposals set forth on the Notice of Annual General
Meeting of Shareholders.

     The Common Shares are listed on the American Stock Exchange ("AMEX") under
the symbol "NAT" and on the Oslo Stock Exchange ("OSE") under the symbol "NAT."

REVOCABILITY OF PROXIES
-----------------------

     A shareholder giving a proxy may revoke it at any time before it is
exercised. A proxy may be revoked by filing with the Secretary of the Company at
the Company's registered office, Canon's Court, 22 Victoria Street, Hamilton HM
12, Bermuda, a written notice of revocation by a duly executed proxy bearing a
later date, or by attending the Meeting and voting in person.

                                  PROPOSAL ONE

                             ELECTION OF DIRECTORS

     The Company currently has five directors. As provided in the Company's
Bye-Laws, each Director is elected at each Annual General Meeting of
shareholders and shall hold office until his successor is elected or appointed
or until his earlier resignation or removal. The Board of Directors has
nominated the five persons listed below, all of whom are current members of the
Board, for election as directors of the Company.

     Set forth below is information concerning each nominee for Director.

     Unless the proxy is marked to indicate that such authorization is expressly
withheld, the persons named in the enclosed proxy intend to vote the shares
authorized thereby FOR the election of the following five nominees. It is
expected that each of these nominees will be able to serve, but if before the
election it develops that any of the nominees are unavailable, the persons named
in the accompanying proxy will vote for the election of such substitute nominee
or nominees as the current Board of Directors may recommend.

Nominees For Election To The Company's Board Of Directors

     Information concerning the nominees for directors of the Company is set
forth below:

           Name                   Age            Position
           ----                   ---            --------

     Herbjorn Hansson             56             Chairman, Chief Executive
                                                 Officer, President and Director

     Hon. Sir David Gibbons       76             Director

     George C. Lodge              76             Director

     Andreas Ove Ugland           49             Director

     Torbjorn Gladso              57             Director

     Herbjorn Hansson has been President and Chief Executive Officer of the
Company since July 1995. He is a major shareholder and Deputy Chairman of
Scandic American Shipping Ltd. ("Scandic"), the Company's manager. He has been
President and Chief Executive Officer of Ugland Nordic Shipping ASA (the "Former
Manager"), the Company's previous manager, since September 1993. Mr. Hansson has
served as a director of the Company since July 1995 and as a director of the
Former Manager, since its organization in June 1989. Mr. Hansson served as the
Chairman of the Board of the Former Manager from June 1989 to September 1993.
Mr. Hansson has been involved in various aspects of the shipping industry and
international finance since the early 1970s, including serving as Chief
Economist of Intertanko, the International Association of Tanker Owners and
independent operators, from 1975-1980. He was an officer of the Anders
Jahre/Kosmos Group from 1980 to 1989, serving as Chief Financial Officer from
1983 to 1988.

     Sir David Gibbons has been a director of the Company since September1995.
Sir David served as the Prime Minister of Bermuda from August 1977 to January
1982. Sir David has served as Chairman of The Bank of N.T. Butterfield and Son
Limited from 1986 to 1997, Chairman of Colonial Insurance Co. Ltd. since 1986
and as Chief Executive Officer of Edmund Gibbons Ltd. since 1954.

     George C. Lodge has been a director of the Company since September 1995.
Professor Lodge has been a member of the Harvard Business School faculty since
1963. He was named associate professor of business administration at Harvard in
1968 and received tenure in 1972.

     Andreas Ove Ugland has been a director of the Company since February 1997.
Mr. Ugland has also served as director and Chairman of: Ugland International
Holding Plc, a shipping/transport company listed on the London Stock Exchange,
Andreas Ugland & Sons AS, Grimstad, Norway, H0egh Ugland Autoliners AS, Oslo and
Buld Associates Inc., Bermuda. Mr. Ugland has had his whole career in shipping
in the Ugland family owned shipping group. Mr. Ugland is controlling shareholder
and Chairman of Scandic.

     Torbjorn Gladso has been a director of the Company since October 2003. Mr.
Glads0 is a partner in Saga Corporate Finance AS. He has extensive experience
within investment banking since 1978. He has been the Chairman of the Board of
the Norwegian Register of Securities and Vice Chairman of the Board of Directors
of the Oslo Stock Exchange.

     Required Vote. Approval of Proposal One will require the affirmative vote
of the majority of the votes cast by shareholders entitled to vote in the
election.

     Audit Committee. In accordance with the rules of the AMEX, the Company's
Board of Directors has established an Audit Committee, consisting of two
independent directors. The members of the Audit Committee are Messrs. Glads0 and
Lodge.

     Officers. Mr. Hansson serves as the Company's President and Chief Executive
Officer. Peter Bubenzer, who is Managing Partner of the Company's Bermuda law
firm, Appleby Spurling Hunter, serves as the Company's Secretary. Mr. Bubenzer
is also a director and Secretary of Scandic.

     THE BOARD OF DIRECTORS UNANIMOUSLY RECOMMENDS A VOTE IN FAVOR OF THE
PROPOSED DIRECTORS. UNLESS REVOKED AS PROVIDED ABOVE, PROXIES RECEIVED BY
MANAGEMENT WILL BE VOTED IN FAVOR OF ALL SUCH PROPOSED DIRECTORS UNLESS A
CONTRARY VOTE IS SPECIFIED.

                                  PROPOSAL TWO

                           APPROVAL OF APPOINTMENT OF
                              INDEPENDENT AUDITORS

     The Board is submitting for approval at the Meeting the selection of
Deloitte & Touche as the Company's independent auditors for the fiscal year
2004. The Board will also lay before the Meeting the Company's audited financial
statements for the year ended December 31, 2003. These financial statements are
being distributed to shareholders as part of the Company's 2003 Annual Report.

     Deloitte & Touche has advised the Company that the firm does not have any
direct or indirect financial interest in the Company, nor has such firm had any
such interest in connection with the Company during the past three fiscal years
other than in its capacity as the Company's independent auditors.

     All services rendered by the independent auditors are subject to review by
the Audit Committee.

     Required Vote. Approval of Proposal Two will require the affirmative vote
of the majority of the votes cast by shareholders entitled to vote in the
election.

THE BOARD OF DIRECTORS UNANIMOUSLY RECOMMENDS A VOTE FOR APPROVAL OF THE
APPOINTMENT OF DELOITTE & TOUCHE AS INDEPENDENT AUDITORS OF THE COMPANY FOR THE
2004 FISCAL YEAR. UNLESS REVOKED AS PROVIDED ABOVE, PROXIES RECEIVED BY
MANAGEMENT WILL BE VOTED IN FAVOR OF SUCH APPROVAL UNLESS A CONTRARY VOTE IS
SPECIFIED.

SOLICITATION
------------

     The cost of preparing and soliciting proxies will be borne by the Scandic.
Solicitation will be made primarily by mail, but shareholders may be solicited
by telephone, telegraph, or personal contact. The Board of Directors may retain
the services of Mellon Investor Services LLC for soliciting proxies from those
entities holding shares in street name.

EFFECT OF ABSTENTIONS
---------------------

     Abstentions will not be counted in determining whether Proposals One or Two
have been approved.

                                  OTHER MATTERS

     No other matters are expected to be presented for action at the Meeting.

                                          By Order of the Directors


                                          Peter Bubenzer
                                          Secretary

May 12, 2004
Hamilton, Bermuda


                                   SIGNATURES

          Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.

                     NORDIC AMERICAN TANKER SHIPPING LIMITED
                                  (registrant)


Dated: May 20, 2004                      By: /s/ Herbjorn Hansson
                                             ----------------------------
                                             Herbjorn Hansson
                                             Chairman, Chief Executive Officer
                                             and President