PRICING SUPPLEMENT NO. 46                                        Rule 424(b)(3)
DATED: May 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: $50,000,000   Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date: 5/18/2001  Fixed Rate Notes [ ]     Certificated Notes [ ]

Maturity Date:  5/17/2002       CUSIP#: 073928UD3

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

[x]   Federal Funds 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: 4.2625%           Interest Payment Period: Quarterly

Index Maturity:  N/A

Spread (plus or minus):  + 0.20%

*    On the 17th of each August, November, February and at Maturity.

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