<PAGE>

                                                                   EXHIBIT 31(b)

     I, Arthur B. Winkleblack, Director, Vice President, and Chief Financial
Officer of H. J. Heinz Finance Company certify that:

     1. I have reviewed this quarterly report on Form 10-Q of H. J. Heinz
Finance Company;

     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 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 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)) 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) [Paragraph omitted pursuant to SEC Release Nos. 33-8238 and
     34-47986;]

          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;

          d) Disclosed in this report any change in the registrant's internal
     control over financial reporting that occurred during the period covered by
     this 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 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: March 7, 2005

                                          By:    /s/ ARTHUR B. WINKLEBLACK
                                            ------------------------------------
                                            Name:    Arthur B. Winkleblack
                                            Title:   Director, Vice President,
                                                     and
                                                     Chief Financial Officer