POWER OF ATTORNEY

KNOW ALL BY THESE PRESENTS, that the undersigned hereby authorizes Stephen A.
Remondi of Exa Corporation, a Delaware corporation (the "Company"), and John D.
Patterson, Jr., Robert W. Sweet, Jr. and Daniel S. Clevenger of Foley Hoag LLP,
each acting singly, to execute for and on behalf of the undersigned, in the
undersigned's capacity as a director or executive officer of the Company, Forms
3, 4 and 5, and any amendments thereto, and cause such form(s) to be filed with
the United States Securities and Exchange Commission pursuant to Section 16(a)
of the Securities Exchange Act of 1934, relating to the undersigned's beneficial
ownership of securities in the Company. The undersigned hereby grants to the
attorney-in-fact full power and authority to do and perform any and every act
and thing whatsoever requisite, necessary or proper to be done in the exercise
of any of the rights and powers herein granted, as fully to all intents and
purposes as the undersigned might or could do personally present, with full
power of substitution, resubstitution or revocation, hereby ratifying and
confirming all that such attorney-in-fact, or such attorney's-in-fact substitute
or substitutes, shall lawfully do or cause to be done by virtue of this power of
attorney and the rights and powers herein granted. The undersigned acknowledges
that the foregoing attorney-in-fact, in serving in such capacity at the request
of the undersigned, is not assuming, nor is the Company assuming, any of the
undersigned's responsibilities to comply with Section 16 of the Securities
Exchange Act of 1934.

This Power of Attorney revokes the authority of any person named in any prior
power of attorney relating to the undersigned's filing obligations pursuant to
Section 16(a) of the Securities Exchange Act of 1934, relating to the
undersigned's beneficial ownership of securities in the Company.  This Power of
Attorney shall remain in full force and effect until the undersigned is no
longer required to file Forms 3, 4 and 5 with respect to the undersigned's
holdings of, and transactions in, securities issued by the Company, unless
earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorney-in-fact.

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 20th day of January, 2016.

                                            /s/ Richard F. Gilbody
                                            --------------------------------
                                            Richard F. Gilbody