PRICING SUPPLEMENT NO. 6                                          Rule 424(b)(3)
DATED: May 21, 2003                                          File No. 333-104455
(To Prospectus dated April 24, 2003,
and Prospectus Supplement dated April 24, 2003)

                                 $10,227,293,162
                         THE BEAR STEARNS COMPANIES INC.
                           Medium-Term Notes, Series B

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

Original Issue Date: 6/27/2003   Fixed Rate Notes [x]     Certificated Notes [ ]

Maturity Date:  6/27/2018        CUSIP#:  073928ZN6

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:    4.20% from and including 6/27/03, to but excluding 6/27/08
                  6.20% from and including 6/27/08, to but excluding 6/27/18

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 June 27, 2006 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 December 27, 2003 and on the 27th of each June and December
   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.