FORM 4 Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940

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(Print or Type Responses)

1. Name and Address of Reporting Person * CLEMENTS ROBERT   2. Issuer Name and Ticker or Trading Symbol ARCH CAPITAL GROUP LTD [ACGL] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director _____ 10% Owner _____ Officer (give title below) __X__ Other (specify below) Chairman of the Board of Direc (Last) (First) (Middle) ARCH CAPITAL GROUP (U.S.) INC., 20 HORSENECK LANE 3. Date of Earliest Transaction (Month/Day/Year) 12/14/2004 (Street) GREENWICH, CT 06830 4. If Amendment, Date Original Filed(Month/Day/Year) 6. Individual or Joint/Group Filing(Check Applicable Line) _X_ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person (City) (State) (Zip) Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned

1.Title of Security (Instr. 3) 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price Common Shares, $.01 par value per share 12/14/2004   S   5,600 D $ 38.6 545,708 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   246 D $ 38.61 545,462 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   900 D $ 38.62 544,562 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   400 D $ 38.63 544,162 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   400 D $ 38.7 543,762 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   3,200 D $ 38.75 540,562 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   600 D $ 38.76 539,962 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   200 D $ 38.77 539,762 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   600 D $ 38.78 539,162 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   400 D $ 38.79 538,762 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   600 D $ 38.8 538,162 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   2,254 D $ 38.81 535,908 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   4,200 D $ 38.85 531,708 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   2,500 D $ 38.86 529,208 I See footnote 1 (1) Common Shares, $.01 par value per share 12/14/2004   S   3,500 D $ 38.9 525,708 I See footnote 1 (1) Common Shares, $.01 par value per share               601,220 D   Common Shares, $.02 par value per share               24,381 I See footnote 2 (2) Common Shares, $.01 par value per share               2,725 I See footnote 3 (3)

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)

1. Title of Derivative Security (Instr. 3)

2. Conversion or Exercise Price of Derivative Security

3. Transaction Date (Month/Day/Year)

3A. Deemed Execution Date, if any (Month/Day/Year)

4. Transaction Code (Instr. 8)

5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5)

6. Date Exercisable and Expiration Date (Month/Day/Year)

7. Title and Amount of Underlying Securities (Instr. 3 and 4)

8. Price of Derivative Security (Instr. 5)

9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)

10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)

11. Nature of Indirect Beneficial Ownership (Instr. 4)

Code

V

(A)

(D)

Date Exercisable

Expiration Date

Title

Amount or Number of Shares

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
CLEMENTS ROBERT ARCH CAPITAL GROUP (U.S.) INC. 20 HORSENECK LANE GREENWICH, CT 06830	X			Chairman of the Board of Direc

Signatures

/s/ Louis T. Petrillo, Attorney-in-fact		12/16/2004
**Signature of Reporting Person		Date

Explanation of Responses:

*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1)	Reflects a sale of Common Shares of Issuer held directly by the Reporting Person's spouse. The Reporting Person disclaims beneficial ownership of securities owned by his spouse.
(2)	Reflects Common Shares held by a grantor retained annuity trust established by the Reporting Person and his spouse, as trustees.
(3)	Reflects Common Shares held by Sound View Partners, L.P. ("Sound View"). The Reporting Person does not have a pecuniary interest in, and disclaims beneficial ownership of, approximately 98% of the securities held by Sound View, which represents the ownership percentage of Sound View partners other than the Reporting Person, but excluding that portion of Sound View held by Taracay Investors ("Taracay") to the extent of the Reporting Person's beneficial ownership of Taracay. Taracay owns approximately 50% of Sound View. Taracay is a general partnership, the general partners of which consist of the Reporting Person and members of his family and the managing partner of which is the Reporting Person.

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