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 * MCCARTER JOHN W JR   2. Issuer Name and Ticker or Trading Symbol GRAINGER W W INC [GWW] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director _____ 10% Owner _____ Officer (give title below) _____ Other (specify below) (Last) (First) (Middle) 100 GRAINGER PARKWAY 3. Date of Earliest Transaction (Month/Day/Year) 06/01/2005 (Street) LAKE FOREST, IL 60045-5201 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 Stock               12,540 D

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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

Stock Units

(1)

06/01/2005

A

23

(2)

(2)

Common Stock

23

$ 54.39

5,402

D

Stock Option

$ 37.25

04/30/2000

04/29/2007

Common Stock

2,200

2,200

D

Stock Option

$ 51.6875

04/29/2001

04/28/2008

Common Stock

1,460

1,460

D

Stock Option

$ 48.625

04/28/1999

04/27/2009

Common Stock

1,860

1,860

D

Stock Option

$ 43.5

04/26/2000

04/25/2010

Common Stock

2,070

2,070

D

Stock Option

$ 37.5

04/25/2001

04/24/2011

Common Stock

2,400

2,400

D

Stock Option

$ 54.61

04/24/2002

04/23/2012

Common Stock

1,650

1,650

D

Stock Option

$ 45.5

04/30/2003

04/29/2013

Common Stock

1,980

1,980

D

Stock Option

$ 54.14

04/28/2004

04/27/2014

Common Stock

1,670

1,670

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
MCCARTER JOHN W JR 100 GRAINGER PARKWAY LAKE FOREST, IL 60045-5201	X

Signatures

L. M. Trusdell, as attorney-in-fact		06/01/2005
**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)	1-for-1
(2)	The Stock Units are expected to settle in cash following termination of service as a director.

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