<PAGE>
                                                                    EXHIBIT 31.1

                                 CERTIFICATIONS

I, A. Roland Thomas, certify that:

1. I have reviewed this quarterly report on Form 10-Q of Moldflow Corporation;

2. Based on my knowledge, this 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 report;

3. Based on my knowledge, the consolidated financial statements, and other
financial information included in this 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 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 15(d)-15(f)) for the
registrant and 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 the 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 control 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 control
over financial reporting.

Date: May 10, 2006

                                    /s/ A. ROLAND THOMAS
                                    -------------------------------------------
                                    A. Roland Thomas
                                    President and Chief Executive Officer
                                    (Principal Executive Officer)