PRICING SUPPLEMENT NO. 35                                         Rule 424(b)(3)
DATED: September 19, 2002                                     File No. 333-76894
(To Prospectus dated January 25, 2002,
and Prospectus Supplement dated January 25, 2002)

                                 $10,006,693,162
                         THE BEAR STEARNS COMPANIES INC.
                           MEDIUM-TERM NOTES, SERIES B

Principal Amount: $25,000,000    Floating Rate Notes    [x] Book Entry Notes [x]

Original Issue Date: 9/24/2002   Fixed Rate Notes [ ]   Certificated Notes [ ]

Maturity Date: 3/24/2004         CUSIP#: 073928XR9

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

[x] Federal Funds Open Rate             Interest Reset Date(s): Daily

[ ] Treasury Rate                       Interest Reset Period: Daily

[ ] LIBOR Reuters                       Interest Payment Date(s): *

[ ] LIBOR Telerate

[ ] Prime Rate

[ ] CMT Rate

Initial Interest Rate: 2.0075%          Interest Payment Period: Quarterly

Index Maturity: N/A

Spread (plus or minus): + 0.32%

*     On the 24th of each June, September, December and March, including the
      maturity date.

The distribution of Notes will conform to the requirements set forth in Rule
2720 of the NASD Conduct Rules.