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EXHIBIT 31.1 CERTIFICATION OF CHIEF EXECUTIVE OFFICER
PURSUANT TO SECTION 302 OF
THE SARBANES-OXLEY ACT OF 2002 I, D. Keith Grossman, certify that: 1. I have reviewed this quarterly report on Form 10-Q of Thoratec Corporation; 2. Based on my knowledge, this quarterly report does not contain any untrue statement of a material
fact or omit to state a material fact necessary to make the statements made, in light of the
circumstances under which such statements were made, not misleading with respect to the period
covered by this quarterly report; 3. Based on my knowledge, the financial statements, and other financial information included in
this quarterly report, fairly present in all material respects the financial condition, results of
operations and cash flows of the registrant as of, and for, the periods presented in this quarterly
report; 4. The registrants other certifying officers and I are responsible for establishing and
maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and
15d-15(e)) and internal control over financial
reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and we
have: a) designed such disclosure controls and procedures, or caused such disclosure controls and
procedures to be designed under our supervision, to ensure that material information relating to
the registrant, including its consolidated subsidiaries, is made known to us by others within those
entities, particularly during the period in which this report is being prepared; b) designed such internal control over financial reporting, or caused such internal control
over financial reporting to be designed under our supervision, to provide reasonable assurance
regarding the reliability of financial reporting and the preparation of financial statements for
external purposes in accordance with generally accepted accounting principles; c) evaluated the effectiveness of the registrants disclosure controls and procedures and
presented in this report our conclusions about the effectiveness of the disclosure controls and
procedures, as of the end of the period covered by this report based on such evaluation; and d) disclosed in this report any change in the registrants internal control over financial
reporting that occurred during the registrants most recent fiscal quarter (the registrants fourth
fiscal quarter in the case of an annual report) that has materially affected, or is reasonably
likely to materially affect, the registrants internal control over financial reporting; 5. The registrants other certifying officers and I have disclosed, based on our most recent
evaluation, to the registrants auditors and the audit committee of registrants board of directors
(or persons performing the equivalent functions): a) all significant deficiencies and material weaknesses in the design or operation of internal
controls which are reasonably likely to adversely affect the registrants ability to record,
process, summarize and report financial information; and b) any fraud, whether or not material, that involves management or other employees who have a
significant role in the registrants internal controls over financial reporting. /s/ D. Keith GrossmanD. Keith GrossmanChief Executive OfficerMay 11, 2005