<PAGE>


                                                                   Exhibit 23(b)


                    Consent of Certified Public Accountants

Board of Directors
CoreStates Financial Corp

We consent to the inclusion of those reports described below under the caption
Reports, in the December 31, 1997 Form 10-K in the following registration
statements of CoreStates Financial Corp:

  (a) The Registration Statement (Form S-8, No. 33-5874), in Post-Effective
      Amendment No. 1 to the Registration Statement (Form S-8, No. 2-91176), the
      Registration Statement (Form S-8, No. 33-28808) and in the related
      prospectuses, each pertaining to the CoreStates Financial Corp Long-Term
      Incentive Plan,

  (b) The Registration Statement (Form S-8, No. 33-32934) and prospectus
      relating to shares of the Corporation's Common Stock issuable under the
      CoreStates Employee Stock Ownership and Savings Plan,

  (c) The Registration Statement (Form S-3, No. 33-50324) pertaining to the
      CoreStates Financial Corp 1992 Long-Term Incentive Plan,

  (d) The Registration Statement (Form S-3, No. 33-57034) and prospectus and
      prospectus supplement pertaining to $1,000,000,000 in aggregate amount of
      Debt Securities issuable by CoreStates Capital Corp and the related
      guarantees of the Corporation, and Preferred Stock, Depository Shares,
      Common Stock, and Capital Securities, issuable by the Corporation,

  (e) The Registration Statement (Form S-3, No. 33-54049) and prospectus and
      prospectus supplement pertaining to $1,000,000,000 in aggregate amount of
      Debt Securities and warrants issuable by CoreStates Capital Corp and the
      related guarantees of the Corporation and Preferred Stock, Depository
      Shares and Common Stock issuable by the Corporation,

  (f) The Registration Statement (Form S-4, as amended by Form S-8, No.
      33-48422) and prospectus relating to shares of the Corporation's Common
      Stock issuable upon the exercise of stock options, the obligations in
      respect to which were assumed by the Corporation in connection with the
      acquisition of First Peoples Corporation,

  (g) The Registration Statement (Form S-4, as amended by Form S-8, No.
      33-51429) and prospectus relating to shares of the Corporation's Common
      Stock issuable upon the exercise of stock options, the obligations in
      respect to which were assumed by the Corporation in connection with the
      acquisition of Constellation Bancorp,

  (h) The Registration Statement (Form S-4, as amended by Form S-8, No. 33-
      53539) and prospectus relating to shares of the Corporation's Common Stock
      issuable upon the exercise of stock options, the obligations in respect to
      which were assumed by the Corporation in connection with the acquisition
      of Independence Bancorp, Inc.,

                                       1

<PAGE>


  (i) The Registration Statement (Form S-4, as amended by Form S-8, No.
      33-55505) and prospectus relating to shares of the Corporation's Common
      Stock issuable upon the exercise of stock options, the obligations in
      respect to which were assumed by the Corporation in connection with the
      acquisition of Germantown Savings Bank,

  (j) The Registration Statement (Form S-4, as amended by Form S-8, No. 33-
      300067) and prospectus relating to shares of the Corporation's Common
      Stock issuable upon the exercise of stock options, the obligations in
      respect to which were assumed by the Corporation in connection with the
      acquisition of Meridian Bancorp, Inc.,

  (k) The Registration Statements (Form S-3, Nos. 33-54049 and 333-2297) and
      prospectus and prospectus supplement pertaining to $1,750,000,000 in
      aggregate amount of Debt Securities issuable by CoreStates Capital Corp
      and the related guarantees of the Corporation and Preferred Stock,
      Depository Shares and Common Stock issuable by the Corporation,

  (l) The Registration Statement (Form S-3, No. 033-40717) and prospectus
      relating to shares of the Corporation's Common Stock issuable under the
      Dividend Reinvestment Plan,

  (m) The Registration Statement (Form S-8, No. 333-16569) and prospectus
      relating to shares of the Corporation's Common Stock issuable under the
      QuestPoint Savings Plan,

  (n) The Registration Statement (Form S-8, No. 333-41083) and prospectus
      relating to shares of the Corporation's Amended and Restated Long-Term
      Incentive Plan (1997),

  (o) The Registration Statement (Form S-8, No. 33-27725) and prospectus
      relating to shares of the Corporation's Amended and Restated Stock
      Compensation Plan for Non-Employee Directors (1997).

                                    Reports
                                    -------

Our report dated January 17, 1996, except as to Note 2, which is as of February
23, 1996, with respect to the consolidated balance sheet of Meridian Bancorp,
Inc. and subsidiaries as of December 31, 1995, and the related consolidated
statements of income, changes in shareholders' equity and cash flows for the
year ended December 31, 1995.

Our report dated January 16, 1996, except as to Note 20, which is as of February
23, 1996, with respect to the consolidated balance sheet of United Counties
Bancorporation and subsidiaries as of December 31, 1995, and the related
consolidated statements of income, changes in stockholders' equity and cash
flows, for the year ended December 31, 1995.

                                            /s/ KPMG Peat Marwick LLP

Philadelphia, Pennsylvania
March 27, 1998

                                       2