Exhibit 31.1
                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER



In connection with the filing of the Quarterly Report on Form 10-Q for the
quarter ended June 30, 2004 by Kirby Corporation, Joseph H. Pyne, President and
Chief Executive Officer, certifies that:

         1.   I have reviewed this quarterly report on Form 10-Q of Kirby
              Corporation (the "Company");

         2.   Based on my knowledge, this quarterly report does not contain any
              untrue statement of a material fact or omit to state a material
              fact necessary to make the statements made, in light of the
              circumstances under which such statements were made, not
              misleading with respect to the period covered by this quarterly
              report;

         3.   Based on my knowledge, the financial statements, and other
              financial information included in this quarterly report, fairly
              present in all material respects the financial condition, results
              of operations and cash flows of the Company as of, and for, the
              periods presented in this quarterly report;

         4.   The Company's other certifying officer and I are responsible for
              establishing and maintaining disclosure controls and procedures
              (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) for
              the Company and we have:

              a)  Designed such disclosure controls and procedures, or caused
                  such disclosure controls and procedures to be designed under
                  our supervision, to ensure that material information relating
                  to the Company, including its consolidated subsidiaries, is
                  made known to us by others within those entities,
                  particularly during the period in which this quarterly report
                  is being prepared;

              b)  Evaluated the effectiveness of the Company's disclosure
                  controls and procedures and presented in this quarterly
                  report our conclusions about the effectiveness of the
                  disclosure controls and procedures, as of the end of the
                  period covered by this quarterly report based on such
                  evaluation; and

              c)  Disclosed in this quarterly report any change in the
                  Company's internal control over financial reporting that
                  occurred during the Company's most recent fiscal quarter that
                  has materially affected, or is reasonably likely to
                  materially affect, the Company's internal control over
                  financial reporting; and

         5.   The Company's other certifying officer and I have disclosed,
              based on our most recent evaluation of internal control over
              financial reporting, to the Company's auditors and the audit
              committee of the Company's board of directors:

              a)  All significant deficiencies and material weaknesses in the
                  design or operation of internal control over financial
                  reporting which are reasonably likely to adversely affect the
                  Company's ability to record, process, summarize and report
                  financial information; and

              b)  Any fraud, whether or not material, that involves management
                  or other employees who have a significant role in the
                  Company's internal control over financial reporting.

                                                  /s/ JOSEPH H. PYNE
                                        --------------------------------------
                                                    Joseph H. Pyne
                                         President and Chief Executive Officer


Dated:  August 5, 2004