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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 annual report on Form 10-K of Thoratec Corporation;

2.    Based on my knowledge, this annual 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 annual
report;

3.    Based on my knowledge, the financial statements, and other financial
information included in this annual 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 annual report;

4.    The registrant's other certifying officer(s) 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;
and

5.    The registrant's other certifying officer(s) and I have disclosed, based
on our most recent evaluation of internal control over financial reporting, 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 over financial reporting 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 Grossman
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D.  Keith Grossman
Chief Executive Officer
March 16, 2005