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-8 (File Nos. 333-30516, 333-01299, 333-22169, 333-44701, 333-56287, 333-72783, 333-76027, 333-113455 and 333-125108) of Parametric Technology Corporation of our report dated December 14, 2006 relating to the financial statements, management’s assessment of the effectiveness of internal control over financial reporting and the effectiveness of internal control over financial reporting, which appears in this Form 10-K.

/s/ PricewaterhouseCoopers LLP

Boston, Massachusetts

December 14, 2006