EXHIBIT 23.1

Consent of Independent Registered Public Accounting Firm

The Board of Directors

Kirby Corporation:

We consent to the incorporation by reference in the registration statements (No. 333-57625, No. 333-72592, No. 333-129290, No. 333-129333, No. 333-152565, No. 333-152566, No. 333-184598 and No. 333-184599) on Form S-8 and (No. 333-220974 and No. 333-222858) on Form S-3 of Kirby Corporation of our reports dated February 21, 2020, with respect to the consolidated balance sheets of Kirby Corporation and consolidated subsidiaries as of December 31, 2019 and 2018, the related consolidated statements of earnings, comprehensive income, stockholders’ equity, and cash flows for each of the years in the three-year period ended December 31, 2019, and the related notes, and the effectiveness of internal control over financial reporting as of December 31, 2019, which reports appear in the December 31, 2019 annual report on Form 10-K of Kirby Corporation.

Our report dated February 21, 2020 refers to a change to the method of accounting for leases and to the method of accounting for recognizing revenues.

/s/ KPMG LLP

Houston, Texas

February 21, 2020