PRICING SUPPLEMENT NO. 42                                         Rule 424(b)(3)
DATED: May 4, 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:  $25,000,000  Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date:  5/8/2001  Fixed Rate Notes [  ]    Certificated Notes [  ]

Maturity Date:  5/8/2003        CUSIP#: 073928TZ6

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:  4.9875%          Interest Payment Period: Quarterly

Index Maturity:  N/A

Spread (plus or minus):  + 0.55%

* On the 8th of each August, November, February and May, including the maturity
  date.

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