PRICING SUPPLEMENT NO. 81                                         Rule 424(b)(3)
DATED:  November 15, 2001                                     File No. 333-52902
(To Prospectus dated January 11, 2001,
and Prospectus Supplement dated January 11, 2001)

                                 $9,015,893,162
                         THE BEAR STEARNS COMPANIES INC.
                           MEDIUM-TERM NOTES, SERIES B

Principal Amount: $200,000,000   Floating Rate Notes [ ]  Book Entry Notes [x]

Original Issue Date: 11/20/2001  Fixed Rate Notes [x]     Certificated Notes [ ]

Maturity Date:  12/20/2002       CUSIP#: 073928VR1

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:  2.425%

Interest Payment Dates: *

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):

* On June 20, 2002 and at Maturity.

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