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 June 30, 2020 (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/ DAVID W. GRZEBINSKI
	David W. Grzebinski
	President and Chief Executive Officer
	/S/ WILLIAM G. HARVEY
	William G. Harvey
	Executive Vice President and
	Chief Financial Officer
Dated: August 6, 2020