THE BEAR STEARNS COMPANIES INC.
                                  IncomeNotes(SM)
            With Maturities of Nine Months or More from Date of Issue


Registration No. 333-109793
Filed Pursuant to Rule 424(b)(3)
Pricing Supplement No. 31
(To Prospectus dated November 17, 2003,
and Prospectus Supplement dated November 17, 2003)
Trade Date: July 19, 2004
Issue Date: July 22, 2004
The date of this Pricing Supplement is July 19, 2004


Fixed Rate Notes


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                                                                                                                         Interest
                                                      Price to        Discounts &                                         Payment
  CUSIP#      Interest Rate       Maturity Date        Public         Commissions      Reallowance         Dealer        Frequency
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 07387EFR3       6.00%              7/15/2029         100.00%            2.50%           0.350%            98.00%          Semi
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                                                   Subject to Redemption
                                                   ---------------------

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First Interest   First Interest     Survivor's                                                      Aggregate
 Payment Date    Payment Amount       Option     Yes/No      Date and Terms of Redemption       Principal Amount     Net Proceeds
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   1/15/2005         $28.83            Yes        Yes     Commencing on 7/15/2009 and on the         $17,472,000        $17,035,200
                                                          15th of each month thereafter until
                                                          Maturity, the Notes may be called in
                                                          whole at par at the option of the
                                                          Company on ten calendar days notice.
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The distribution of IncomeNotes will conform to the requirements set forth in
Rule 2720 of the NASD Conduct Rules.