Exhibit 23.1 INDEPENDENT AUDITORS' CONSENT We consent to the incorporation by reference in Registration Statements on Form S-3 (No. 333-97783, 333-72128, 333-61136, and 333-32684) and Registration Statements on Form S-8 (No. 333-106238, 333-80807, 333-56212, 333-32223, 333-11883, 33-35549, 33-35719, 33-72502, Post-Effective Amendment No. 1 to Registration Statement No. 333-90768, Post-Effective Amendment No. 1 to Registration Statement No. 2-97542, Post-Effective Amendment No. 1 to Registration Statement No. 2-78926, and Post-Effective Amendment No. 3 to Registration Statement No. 2-78925) of our reports dated March 12, 2004 (which reports express unqualified opinions and include an explanatory paragraph concerning the adoption of a new accounting principle in 2002) appearing in this Annual Report on Form 10-K of Thoratec Corporation for the year ended January 3, 2004. /s/ DELOITTE & TOUCHE LLP San Francisco, California March 17, 2004 78