PRICING SUPPLEMENT NO. 3                                        Rule 424(b)(3)
DATED:   December 4, 2003                                  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:  $5,000,000   Floating Rate Notes [ ]  Book Entry Notes [x]

Original Issue Date:  12/9/2003 Fixed Rate Notes [x]     Certificated Notes  [ ]

Maturity Date:  12/9/2004       CUSIP#: 073928C50

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                 N/A

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

Interest Rate: 1.58%

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):

* June 9, 2004 and at Maturity.

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