1
 
                                                                    EXHIBIT 23.1
 
                         INDEPENDENT AUDITORS' CONSENT
 
     We consent to incorporation by reference in the Registration Statements
(No. 33-62116), (No. 33-56195) on Form S-3 and (No. 33-68140), (No. 2-67954),
(No. 2-84789), (No. 33-57621), (No. 33-57625) on Form S-8 of Kirby Corporation
and consolidated subsidiaries of our report dated February 21, 1995, relating to
the consolidated balance sheets of Kirby Corporation and consolidated
subsidiaries as of December 31, 1994 and 1993, 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, 1994, which report appears in
the December 31, 1994 Annual Report on Form 10-K of Kirby Corporation and
consolidated subsidiaries.
 
                                          KPMG PEAT MARWICK LLP
 
Houston, Texas
March 14, 1995