EXHIBIT 32.1

                   CERTIFICATION OF PERIODIC FINANCIAL REPORT
                       PURSUANT TO 18 U.S.C. SECTION 1350

      The undersigned officer of Moldflow Corporation (the "Company") hereby
certifies that the Company's annual report on Form 10-K for the fiscal year
ended June 30, 2004 to which this certification is being furnished as an exhibit
(the "Report"), as filed with the Securities and Exchange Commission on the date
hereof, fully complies with the requirements of Section 13(a) or 15(d), as
applicable, of the Securities Exchange Act of 1934, as amended (the "Exchange
Act"), and that the information contained in the Report fairly presents, in all
material respects, the financial condition and results of operations of the
Company. This certification is provided solely pursuant to 18 U.S.C. Section
1350 and Item 601(b)(32) of Regulation S-K ("Item 601(b)(32)") promulgated under
the Securities Act of 1933, as amended (the "Securities Act"), and the Exchange
Act. In accordance with clause (ii) of Item 601(b) (32), this certification (A)
shall not be deemed "filed" for purposes of Section 18 of the Exchange Act, or
otherwise subject to the liability of that section, and (B) shall not be deemed
to be incorporated by reference into any filing under the Securities Act or the
Exchange Act, except to the extent that the Company specifically incorporates it
by reference.

Date: September 10, 2004

                                         /s/ A. ROLAND THOMAS
                                         ---------------------------------------
                                         Name:    A. Roland Thomas
                                         Title:   President and Chief
                                                  Executive Officer