Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in the Registration Statements on Form S-3 (No. 333-192745) and S-8 (No. 333-192746 and 333-198403) of Exa Corporation of our report dated March 21, 2016 relating to the financial statements in this Annual Report on Form 10-K. We also consent to the incorporation by reference of our report dated March 21, 2016 relating to the financial statement schedule, which appears in this Form 10-K.

/s/ PricewaterhouseCoopers LLP

Boston, Massachusetts

March 21, 2016