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. 33
(To Prospectus dated November 17, 2003,
and Prospectus Supplement dated November 17, 2003)
Trade Date: August 2, 2004
Issue Date: August 5, 2004
The date of this Pricing Supplement is August 2, 2004



Fixed Rate Notes
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                                                                                                              Interest
                                                  Maturity   Price to   Discounts &                            Payment
   CUSIP#               Interest Rate               Date       Public   Commissions  Reallowance    Dealer    Frequency
-------------------------------------------------------------------------------------------------------------------------
                                                                                         
  07387EFT9   5.00% from and including 8/5/04,   8/15/2019    100.00%     2.00%         0.350%      98.40%     Monthly
              to but excluding 8/15/07.
              6.05% from and including 8/15/07,
              to but excluding 8/15/19.
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  07387EFU6                 6.00%                8/15/2029    100.00%     2.50%         0.350%      98.00%      Semi
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                                         Subject to Redemption
                                         ---------------------
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                    First
                  Interest                                                                     Aggregate
First Interest     Payment   Survivor's                                                        Principal
 Payment Date      Amount      Option    Yes/No         Date and Terms of Redemption            Amount      Net Proceeds
--------------------------------------------------------------------------------------------------------------------------
                                                                                           
   9/15/2004        $5.56        Yes       Yes   The Notes may be called in whole at par,      $1,297,000    $1,271,060
                                                 one time only on 8/15/2007, at the option
                                                 of the Company on ten calendar days notice.
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   2/15/2005       $26.67        Yes       Yes   Commencing on 8/15/2009 and on the 15th of
                                                 each month thereafter until Maturity, the
                                                 Notes may be called in whole at par at the    $9,077,000    $8,850,075
                                                 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.