PRICING SUPPLEMENT NO. 42                                       Rule 424(b)(3)
DATED:   December 9, 2004                                  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: $34,000,000    Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date: 12/14/2004  Fixed Rate Notes [ ]     Certificated Notes [ ]


Maturity Date:  12/14/2007       CUSIP#: 073928H89

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

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

[ ]   Treasury Rate                      Interest Reset Period:  Quarterly

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

[x]   LIBOR Telerate

[ ]   Prime Rate

[ ]   CMT Rate

Initial Interest Rate: 2.58%             Interest Payment Period:  Quarterly

Index Maturity:  Three Months

Spread (plus or minus):  +0.10%

*  On the 14th of each March, June, September and December thereafter prior to
   Maturity.

** On the 14th 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.