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 ------------------------------------------------------------------------------------------------------------------------------------ Interest Price to Discounts & Payment CUSIP# Interest Rate Maturity Date Public Commissions Reallowance Dealer Frequency ------------------------------------------------------------------------------------------------------------------------------------ 07387EFR3 6.00% 7/15/2029 100.00% 2.50% 0.350% 98.00% Semi ------------------------------------------------------------------------------------------------------------------------------------ Subject to Redemption --------------------- ------------------------------------------------------------------------------------------------------------------------------------ First Interest First Interest Survivor's Aggregate Payment Date Payment Amount Option Yes/No Date and Terms of Redemption Principal Amount Net Proceeds ------------------------------------------------------------------------------------------------------------------------------------ 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. ------------------------------------------------------------------------------------------------------------------------------------ *** The distribution of IncomeNotes will conform to the requirements set forth in Rule 2720 of the NASD Conduct Rules.