PRICING SUPPLEMENT NO. 2                                          Rule 424(b)(3)
DATED:  December 2, 2003 +                                   File No. 333-109793
        December 3, 2003 ++
(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: $75,000,000   Floating Rate Notes [x]   Book Entry Notes [x]

Original Issue Date: 12/5/2003  Fixed Rate Notes [ ]      Certificated Notes [ ]

Maturity Date: 12/5/2005        CUSIP#: 073928C43

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:  1.18%            Interest Payment Period:  Quarterly

Index Maturity:  N/A

Spread (plus or minus):  +0.18%

+     $25,000,000 was traded on December 2, 2003.
++    $50,000,000 was traded on December 3, 2003.

*     On the 5th of each March, June, September and December, including the
      maturity date.

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