EXHIBIT 23.1

Consent of Independent Registered Public Accounting Firm

The Board of Directors and Stockholders

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 25, 2019, with respect to the consolidated balance sheets of Kirby Corporation and consolidated subsidiaries as of December 31, 2018 and 2017, and 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, 2018, and the related notes (collectively, the consolidated financial statements), and the effectiveness of internal control over financial reporting as of December 31, 2018, which reports appear in the December 31, 2018 annual report on Form 10-K of Kirby Corporation.

Our report dated February 25, 2019, on the effectiveness of internal control over financial reporting as of December 31, 2018, expresses our opinion that Kirby Corporation and consolidated subsidiaries did not maintain effective internal control over financial reporting as of December 31, 2018 because of the effect of a material weakness on the achievement of the objectives of the control criteria and contains an explanatory paragraph that states the Company’s assessment of changes in internal control related to a recently acquired subsidiary’s information technology general controls did not timely identify inappropriate user access issues at the subsidiary. Specifically, the Company did not design and maintain user access controls that adequately restricted user and privileged access to certain IT operating systems, databases and IT applications at this subsidiary.  As a result, process level automated controls and manual controls that are dependent on the completeness and accuracy of information derived from the affected IT systems were also ineffective because they could have been adversely impacted.

/s/ KPMG LLP

Houston, Texas

February 25, 2019