EXHIBIT 32

Parametric Technology Corporation

Certification of Periodic Financial Report

Pursuant to 18 U.S.C. Section 1350

Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, each of the undersigned officers of Parametric Technology Corporation (the “Company”) certifies that, to his knowledge, the Quarterly Report on Form 10-Q of the Company for the quarter ended July 3, 2004 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and information contained in that Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: August 17, 2004	/s/ C. RICHARD HARRISON
	C. Richard Harrison Chief Executive Officer
Date: August 17, 2004	/s/ CORNELIUS F. MOSES, III
	Cornelius F. Moses, III Executive Vice President and Chief Financial Officer