Exhibit 32

Certification Pursuant to Section 18 U.S.C. Section 1350

In connection with the filing of the Quarterly Report on Form 10-Q for the quarter ended March 31, 2011 (the “Report”) by Kirby Corporation (the “Company”), each of the undersigned hereby certifies that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/S/ JOSEPH H. PYNE

Joseph H. Pyne

Chairman and

Chief Executive Officer

/S/ DAVID W. GRZEBINSKI

David W. Grzebinski

Executive Vice President and

Chief Financial Officer

Dated:  May 5, 2011