PRICING SUPPLEMENT NO. 42                                         Rule 424(b)(3)
DATED:  October 18, 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: $15,000,000    Floating Rate Notes [ ]  Book Entry Notes [x]

Original Issue Date: 10/25/2002  Fixed Rate Notes [x]     Certificated Notes [ ]

Maturity Date: 10/25/2017        CUSIP#:  073928XY4

Option to Extend Maturity:       No    [x]
                                 Yes   [ ]  Final Maturity Date:

Minimum Denominations:           $1,000, increased in multiples of $1,000


                                              Optional            Optional
                         Redemption           Repayment           Repayment
   Redeemable On          Price(s)             Date(s)            Price(s)
   -------------       --------------       -------------        -----------

         *                   N/A                 N/A                 N/A

Applicable Only to Fixed Rate Notes:
------------------------------------

Interest Rate:  6.20%

Interest Payment Date(s):  **

Applicable Only to Floating Rate Notes:
---------------------------------------

Interest Rate Basis:                     Maximum Interest Rate:

[ ]   Commercial Paper Rate              Minimum Interest Rate:

[ ]   Federal Funds Effective Rate

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

[ ]   Treasury Rate                      Interest Reset Period:

[ ]   LIBOR Reuters                      Interest Payment Date(s):

[ ]   LIBOR Telerate

[ ]   Prime Rate

[ ]   CMT Rate

Initial Interest Rate:                   Interest Payment Period:

Index Maturity:

Spread (plus or minus):

*     Commencing October 25, 2005 and on the interest payment dates thereafter
      until Maturity, the Notes may be called in whole at par at the option of
      the Company on ten calendar days notice.

**    Commencing November 25, 2002 and on the 25th of each month thereafter
      until Maturity or until the Notes are called.

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