PRICING SUPPLEMENT NO. 31 Rule 424(b)(3) DATED: September 1, 2004 File No. 333-109793 (To Prospectus dated November 17, 2003, and Prospectus Supplement dated November 17, 2003) $10,668,950,162 THE BEAR STEARNS COMPANIES INC. Medium-Term Notes, Series B Principal Amount: $400,000,000 Floating Rate Notes [x] Book Entry Notes [x] Original Issue Date: 9/9/2004 Fixed Rate Notes [ ] Certificated Notes [ ] Maturity Date: 9/9/2009 CUSIP#: 073928G56 Euroclear and Clearstream Common Code: 020066784 Option to Extend Maturity: No [x] Yes [ ] Final Maturity Date: Optional Optional Redemption Repayment Repayment Redeemable On Price(s) Date(s) Price(s) ------------- -------------- ------------- ----------- N/A N/A N/A N/A Applicable Only to Fixed Rate Notes: ----------------------------------- Interest Rate: Interest Payment Dates: Applicable Only to Floating Rate Notes: -------------------------------------- Interest Rate Basis: Maximum Interest Rate: N/A [ ] Commercial Paper Rate Minimum Interest Rate: N/A [ ] Federal Funds Effective Rate [ ] Federal Funds Open Rate Interest Reset Date(s): * [ ] Treasury Rate Interest Reset Period: Quarterly [ ] LIBOR Reuters Interest Payment Date(s): ** [x] LIBOR Telerate [ ] Prime Rate [ ] CMT Rate Initial Interest Rate: 2.13% Interest Payment Period: Quarterly Index Maturity: Three Months Spread (plus or minus): +0.27% * On the 9th of each December, March, June and September prior to Maturity. ** On the 9th of each December, March, June and September, including the maturity date. The distribution of Notes will conform to the requirements set forth in Rule 2720 of the NASD Conduct Rules.