EXHIBIT 5.1

PALMER & DODGE LLP

111 Huntington Avenue at Prudential Center

Boston, MA 02199-7613

May 18, 2005

Parametric Technology Corporation

140 Kendrick Street

Needham, MA 02494

Ladies and Gentlemen:

We are rendering this opinion in connection with the Registration Statement on Form S-8 (the “Registration Statement”) filed on or about the date hereof with the Securities and Exchange Commission under the Securities Act of 1933, as amended, for the registration of 13,000,000 shares of Common Stock, $.01 par value per share (the “Shares”), of Parametric Technology Corporation, a Massachusetts corporation (the “Company”), issuable upon exercise of options granted or to be granted under the Company’s 2000 Equity Incentive Plan (the “Plan”).

We have acted as your counsel in connection with the preparation of the Registration Statement and are familiar with the proceedings taken by the Company in connection with the authorization, issuance and sale of the Shares. We have examined all such documents as we consider necessary to enable us to render this opinion.

Based upon the foregoing, we are of the opinion that, when issued and sold in accordance with the terms of the Plan, the Shares will be validly issued, fully paid and nonassessable.

We hereby consent to the use of our name in the Registration Statement and consent to the filing of this opinion with the Securities and Exchange Commission as an exhibit to the Registration Statement.

Very truly yours,

/s/ PALMER & DODGE LLP

PALMER & DODGE LLP

Main 617.239.0100 Fax 617.227.4420 www.palmerdodge.com