HMS (HMSY) 10-K 2018 FY Annual report

Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We have issued our reports dated February 25, 2019, with respect to the consolidated financial statements and internal control over financial reporting included in the Annual Report of HMS Holdings Corp. on Form 10-K for the year ended December 31, 2018. We consent to the incorporation by reference of said reports in the Registration Statements of HMS Holdings Corp. on Forms S-8 (File No. 333-161415, 333-149836, 333-139025, 333-178752, 333-183361, and 333-212319).

/s/ Grant Thornton, LLP

Dallas, Texas

February 25, 2019