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 * PYNE J H   2. Issuer Name and Ticker or Trading Symbol KIRBY CORP [KEX] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director _____ 10% Owner __X__ Officer (give title below) _____ Other (specify below) President (Last) (First) (Middle) 55 WAUGH DRIVE, SUITE 1000 3. Date of Earliest Transaction (Month/Day/Year) 11/03/2004 (Street) HOUSTON, TX 77007 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, par value $.10 per share 11/04/2004   M   40,000 A $ 18.0625 171,500 D   Common Stock, par value $.10 per share 11/03/2004 11/04/2004 S   30,000 D $ 43.575 141,500 D   Common Stock, par value $.10 per share               4,404 I 401(k) Plan

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

Employee Stock Option (Right to Buy)

$ 18.0625

11/04/2004

M

40,000

02/10/2003(1)

02/10/2005

Common Stock

40,000

$ 18.0625

693,658

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
PYNE J H 55 WAUGH DRIVE SUITE 1000 HOUSTON, TX 77007	X		President

Signatures

G. Stephen Holcomb, Agent and Attorney-in-Fact		11/05/2004
**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)	Original option of 100,000 shares exercisable 33% after one year, 67% after two years and 100% after three years from date of grant.
Remarks: An option of Mr. Pyne's was exercised on October 6, 2004 for 4,000 shares and, of the exercise, 4,000 shares were registered in the name of his ex-wife pursuant to a domestic relations order.

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