EXHIBIT 23.1

INDEPENDENT REGISTERED PUBLIC ACCOUNTANTS’ CONSENT

      We consent to the incorporation by reference in the registration statement (No. 33-56195) on Form S-3, and the registration statement (No. 33-68140), (No. 33-57621), (No. 33-57625), (No. 333-33913), (No. 333-72592) and (No. 333-100765) on Form S-8 of Kirby Corporation of our reports which appear in the December 31, 2004 annual report on Form 10-K of Kirby Corporation:

•  Dated March 4, 2005, with respect to the consolidated balance sheets of Kirby Corporation as of December 31, 2004 and 2003, and the related consolidated statements of earnings, stockholders’ equity and cash flows for each of the years in the three-year period ended December 31, 2004, and

•  Dated March 4, 2005, with respect to management’s assessment of the effectiveness of internal control over financial reporting as of December 31, 2004 and the effectiveness of internal control over financial reporting as of December 31, 2004.

KPMG LLP

Houston, Texas

March 4, 2005