<PAGE>   1
                                    FORM 10Q
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549



              [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                For the quarterly period ended December 27, 1996
                                               -----------------

                                       OR

              [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                   For the transition period from ____to ____

                          Commission File Number 1-6549
                                                 ------

                     American Science and Engineering, Inc.
             ------------------------------------------------------
             (Exact name of Registrant as specified in its charter)

              Massachusetts                                      04-2240991
    -------------------------------                          -------------------
    (State or other jurisdiction of                           (I.R.S. Employer
     incorporation or organization)                          Identification No.)

         829 Middlesex Turnpike
        Billerica, Massachusetts                                   01821
----------------------------------------                         ----------
(Address of principal executive offices)                         (Zip Code)

                                 (508) 262-8700
              ----------------------------------------------------
              (Registrant's telephone number, including area code)


   ---------------------------------------------------------------------------
   (Former name, former address and former fiscal year, if changed since last
                                    report)

Indicate by check mark whether the Registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months, and (2) has been subject to such filing requirements
for the past 90 days.

                                            Yes  X        No
                                               -----        -----

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date

                                                     Outstanding at
         Class of Common Stock                       Dec. 27, 1996
         ---------------------                       --------------
         $.66 2/3 par value                            4,556,425


                               Page 1 of 10 Pages
                     The Exhibit Index is Located at Page 10


<PAGE>   2



                     AMERICAN SCIENCE AND ENGINEERING, INC.
                         PART I - FINANCIAL INFORMATION
<TABLE>
                                  CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS
                                                    (Unaudited)
<CAPTION>

                                                     
                                                     
                                                           For The Three Months Ended     For The Nine Months Ended    
                                                           --------------------------     ------------------------- 
                                                           Dec. 27,          Dec. 29,     Dec. 27,         Dec. 29,    
Dollars and shares in Thousands, except per share amounts    1996              1995         1996             1995      
                                                           --------          --------     --------         --------
                                                            
<S>                                                         <C>               <C>          <C>              <C>    
NET SALES AND CONTRACT REVENUE                              $7,127            $4,717       $20,511          $12,116
                                                            ------            ------       -------          -------
                                                                                                            
COSTS AND EXPENSES:                                                                                         
  Cost of sales and contracts                                4,295             3,297        13,232            8,327
  Selling, general and administrative expenses               1,696             1,030         4,568            2,951
  Research and development                                     538               113         1,132              296
                                                            ------            ------       -------          -------
  Total costs and expenses                                   6,529             4,440        18,932           11,574
                                                            ------            ------       -------          -------
                                                                                                            
OPERATING INCOME                                               598               277         1,579              542
                                                            ------            ------       -------          -------
                                                                                                            
OTHER INCOME (EXPENSE):                                                                                     
  Interest, net                                                 18                10            88               48
  Other, net                                                   (92)              (35)         (247)            (131)
                                                            ------            ------       -------          -------
  Total other income (expense)                                 (74)              (25)         (159)             (83)
                                                            ------            ------       -------          -------
                                                                                                            
INCOME BEFORE PROVISION                                                                                     
  FOR INCOME TAXES                                             524               252         1,420              459
                                                                                                            
PROVISION FOR INCOME TAXES                                      21                 -            60                -
                                                            ------            ------       -------          -------
                                                                                                            
NET INCOME                                                  $  503            $  252       $ 1,360          $   459
                                                            ======            ======       =======          =======
                                                                                                            
INCOME PER COMMON SHARE AND                                                                                 
  COMMON EQUIVALENT SHARE                                   $  .10            $  .06       $   .28          $   .10
                                                            ======            ======       =======          =======
                                                                                                            
INCOME PER COMMON SHARE,                                                                                    
  ASSUMING FULL DILUTION                                    $  .10            $  .05       $   .28          $   .10
                                                            ======            ======       =======          =======
                                                                                                            
DIVIDENDS PAID PER SHARE                                      NONE              NONE          NONE             NONE
                                                            ======            ======       =======          =======
                                                                                                            
SHARES USED IN INCOME PER SHARE                                                                             
  AND COMMON EQUIVALENT SHARES                               4,822             4,563         4,801            4,473
                                                            ======            ======       =======          =======
                                                                                                            
SHARES USED IN INCOME PER COMMON                                                                            
  SHARE, ASSUMING FULL DILUTION                              4,846             4,605         4,816            4,494
                                                            ======            ======       =======          =======
</TABLE>

The accompanying notes are an integral part of these condensed consolidated
financial statements.

                                       -2

<PAGE>   3



                     AMERICAN SCIENCE AND ENGINEERING, INC.
<TABLE>
                                       CONDENSED CONSOLIDATED BALANCE SHEETS
<CAPTION>



Dollars in Thousands                                                   Dec. 27, 1996       Mar. 29, 1996
                                                                       -------------       -------------
                                                                        (Unaudited)
<S>            <C>                                                        <C>                 <C>    
ASSETS         CURRENT ASSETS:
               Cash and cash equivalents                                  $ 2,115             $ 3,377
               Accounts receivable, net                                     6,036               3,875
               Unbilled costs and fees, net                                   790               1,258
               Inventories                                                  4,420               4,314
               Prepaid expenses and other current assets                      158                 278
               Deferred income taxes                                           10                  10
                                                                          -------             -------
               Total current assets                                        13,529              13,112
                                                                          -------             -------

               NON CURRENT ASSETS:
               Deposits                                                       110                 257
               Property and equipment, net of
                  accumulated depreciation of
                  $8,761 at Dec. 27, 1996 and
                  $8,507 at March 29, 1996                                  1,233                 926
                                                                          -------             -------

                                                                          $14,872             $14,295
                                                                          =======             =======
</TABLE>


The accompanying notes are an integral part of these condensed consolidated
financial statements.

                                       -3

<PAGE>   4



                     AMERICAN SCIENCE AND ENGINEERING, INC.
<TABLE>
                                 CONDENSED CONSOLIDATED BALANCE SHEETS (CONTINUED)
<CAPTION>



Dollars in Thousands                                                     Dec. 27, 1996       Mar. 29, 1996
                                                                         -------------       -------------
                                                                          (Unaudited)
<S>                 <C>                                                     <C>                 <C>    
LIABILITIES &       CURRENT LIABILITIES:
STOCKHOLDERS'       Current maturities of obligations
INVESTMENT            under capital leases                                  $    17             $    16
                    Accounts payable                                          2,309               2,021
                    Accrued legal                                               138                 128
                    Accrued salaries and benefits                               406                 496
                    Accrued warranty costs                                      396                 178
                    Accrued commissions                                         215                 160
                    Deferred revenue                                            841                 375
                    Customer deposits                                           274               2,670
                    Other current liabilities                                   441                 258
                                                                            -------             -------
                    TOTAL CURRENT LIABILITIES                                 5,037               6,302
                                                                            -------             -------

                    NONCURRENT LIABILITIES:
                    Obligations under capital leases, net
                      of current maturities                                      47                  59
                    Deferred compensation                                       182                 192
                    Deferred rent                                               245                 231
                    Deferred income taxes                                        10                  10
                                                                            -------             -------
                    TOTAL NONCURRENT LIABILITIES                                484                 492
                                                                            -------             -------

                    STOCKHOLDERS' INVESTMENT: 
                    Preferred stock, no par value
                    Authorized - 100,000 shares 
                    Issued - None 
                    Common stock, $.66-2/3 par value 
                    Authorized - 8,000,000 shares 
                    Issued 4,556,425 shares at Dec. 27, 1996
                    and 4,500,627 shares at Mar. 29, 1996                     3,041               3,001
                    Capital in excess of par value                           14,992              14,556
                    Accumulated deficit                                      (7,930)             (9,290)
                                                                            -------             -------
                                                                             10,103               8,267
                    Note receivable-Officer                                    (640)               (640)
                    Less: treasury stock -
                    57,907 shares at Dec.27, 1996 and
                      67,377 shares at March 29, 1996 at cost                  (112)               (126)
                                                                            -------             -------

                    TOTAL STOCKHOLDERS' INVESTMENT                            9,351               7,501
                                                                            -------             -------
                                                                            $14,872             $14,295
                                                                            =======             =======
</TABLE>


The accompanying notes are an integral part of these condensed consolidated
financial statements.

                                       -4

<PAGE>   5



                     AMERICAN SCIENCE AND ENGINEERING, INC.
<TABLE>
                                  CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                                                    (Unaudited)
<CAPTION>


Dollars in Thousands                                                             For the Nine Months Ended
                                                                              --------------------------------
                                                                              Dec. 27, 1996      Dec. 29, 1995
                                                                              -------------      -------------
<S>                                                                              <C>                <C>    
CASH FLOWS FROM OPERATING ACTIVITIES:
Net income                                                                       $ 1,360            $   459
Adjustments to reconcile net income to net cash provided by
(used for) operating activities:
   Depreciation and amortization                                                     254                148
   Provisions for contract, restructuring, inventory, accounts
   receivable and warranty reserves                                                  723                 30
Changes in assets and liabilities:
   Accounts receivable                                                            (2,339)            (2,222)
   Unbilled costs and fees                                                           443                741
   Inventories                                                                      (206)                99
   Prepaid expenses and other assets                                                 267               (155)
   Accounts payable                                                                  288               (316)
   Customer deposits                                                              (2,396)                20
   Accrued expenses and other current liabilities                                    679                214
   Noncurrent liabilities                                                              5                  7
                                                                                 -------            -------
   Total adjustments                                                              (2,282)            (1,434)
                                                                                 -------            -------

Net cash used for operating activities                                              (922)              (975)
                                                                                 -------            -------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Purchase of property and equipment                                               (561)                33
                                                                                 -------            -------
   Cash (used for) provided by investing activities                                 (561)                33
                                                                                 -------            -------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Proceeds from borrowings                                                            -                650
   Repayment of officer note                                                           -               (650)
   Proceeds from exercise of stock options                                           232                 40
   Proceeds from issuance of stock                                                     -                902
   Principal payments of capital lease obligations                                   (11)              (156)
                                                                                 -------            -------
   Cash provided by financing activities                                             221                786
                                                                                 -------            -------

NET DECREASE IN CASH AND CASH EQUIVALENTS                                         (1,262)              (156)
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                                   3,377                869
                                                                                 -------            -------
CASH AND CASH EQUIVALENTS AT END OF PERIOD                                       $ 2,115            $   713
                                                                                 =======            =======

SUPPLEMENTAL DISCLOSURES OF CASH FLOW
INFORMATION:
   Interest paid                                                                 $     8            $    47
   Income taxes paid                                                             $    30            $     -
                                                                                                    
NON-CASH TRANSACTIONS:                                                                              
   Issuance of stock in lieu of fees                                             $   258            $     -
</TABLE>

The accompanying notes are an integral part of these condensed consolidated
financial statements.

                                       -5

<PAGE>   6



                     AMERICAN SCIENCE AND ENGINEERING, INC.
           PREPARATION OF CONDENSED CONSOLIDATED FINANCIAL STATEMENTS


The condensed consolidated financial statements included herein have been
prepared by American Science and Engineering, Inc. (the Company) pursuant to the
rules and regulations of the Securities and Exchange Commission, and the annual
condensed consolidated financial statements are subject to year end audit by
independent public accountants. Certain information and footnote disclosures
normally included in financial statements prepared in accordance with generally
accepted accounting principles have been condensed or omitted pursuant to such
rules and regulations. The Company believes, however, that the disclosures are
adequate to make the information presented not misleading. It is suggested that
these condensed consolidated financial statements be read in conjunction with
the consolidated financial statements and the notes thereto included in the
Company's latest annual report on Form 10-K.

The condensed consolidated financial statements, in the opinion of management,
include all adjustments necessary to present fairly the Company's financial
position and the results of operations. These results are not necessarily to be
considered indicative of the results for the entire year.


NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS (Unaudited)

1.       Nature of Operations and Significant Accounting Policies
         --------------------------------------------------------
         American Science and Engineering, Inc., is engaged in the development
         and manufacture of sophisticated X-ray inspection systems for critical
         detection and security screening solutions for sale primarily to U.S.
         and foreign government agencies.

         The significant accounting policies followed by the Company and its
         subsidiary in preparing its consolidated financial statements are set
         forth in Note 1 to the consolidated financial statements included in
         Form 10-K for the year ended March 29, 1996. The Company has made no
         change in these policies during this quarter.

<TABLE>
2.       Inventories
         -----------
         Inventories consisted of:
<CAPTION>

                                             Dec. 27, 1996        Mar. 29, 1996
                                             -------------        -------------
    <S>                                        <C>                  <C>       
    Raw materials and completed
       sub-assemblies                          $3,018,000           $3,014,000
    Work in process                             1,402,000            1,300,000
                                               ----------           ----------
    Total                                      $4,420,000           $4,314,000
                                               ==========           ==========
</TABLE>

3.       Income per Common and Common Equivalent Share
         ---------------------------------------------
         Income per common share for the nine month period ended December 27,
         1996, was computed by dividing net income by the weighted average
         number of common stock and common stock equivalents outstanding during
         the year. If dilutive, stock options and stock warrants were considered
         in the computation of earnings per common and common equivalent shares.



                                       -6

<PAGE>   7



                     AMERICAN SCIENCE AND ENGINEERING, INC.
           PREPARATION OF CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                                   (Continued)


<TABLE>
4.       Income Taxes
         ------------
         At March 29, 1996, the Company had approximately $8,989,000 of federal
         net operating loss carryforwards which can be used, subject to certain
         limitations, to offset future federal taxable income. The carryforwards
         expire beginning in the year 1998 through the year 2010. The Company
         also has unused investment tax and other credits of approximately
         $235,000 expiring from 1997 through 2001. The provision for income
         taxes in the accompanying statement of income is substantially a
         current provision and differs from the provision calculated by applying
         the statutory federal income tax rate of 34% to income before provision
         for income taxes due to the following:
<CAPTION>


                                                           Nine Months Ended
                                                             Dec. 27, 1996
                                                           -----------------
    <S>                                                        <C>      
    Provision for income taxes at statutory rate               $ 483,000
    Benefit from net operating loss carryforward                (483,000)
    Other tax liabilities                                         60,000
                                                               ---------
                                                               $  60,000
                                                               =========
</TABLE>


                                       -7

<PAGE>   8



                     AMERICAN SCIENCE AND ENGINEERING, INC.
           ITEM 2 - MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                       CONDITION AND RESULTS OF OPERATIONS


Overview
--------
In the third quarter of fiscal 1997, the Company produced its seventh
consecutive quarter of increasing profits. Net sales and contract revenues were
$7,127,000 during the quarter, a 51% increase from the comparable year ago
period and a 7% increase from the second quarter of fiscal 1997. The company
earned net profits of $503,000 in the current quarter, a 100% increase compared
to net profits of $252,000 in the corresponding year ago period and a 12%
increase compared to net profits of $451,000 in the previous quarter.

Results of Operations
---------------------
Net sales and contract revenues of $7,127,000 in the third quarter increased by
$2,410,000 (51%) in comparison to the corresponding period a year ago and
increased by $442,000 (7%) compared to the second quarter of fiscal year 1997.
Compared to the previous quarter, security systems and related field service
revenues were higher by $618,000 (10%) and research and engineering revenues
were lower by $176,000 (32%). During the quarter, the Company shipped a large
volume of security systems, contributing to the largest quarterly revenue level
in nearly 11 years.

For the third quarter, costs of sales and contracts increased to $4,295,000 from
$3,297,000 in the corresponding period a year ago primarily due to increased
sales volume of X-ray inspection systems and field service revenues in the
current period. Costs of sales and contracts represented 60% of revenues versus
70% for the corresponding period last year and 65% for the second quarter of
fiscal year 1997. Costs of sales as a percentage of revenues in the current
quarter decreased over the previous quarter primarily due to increased volume
and a change in the sales mix.

Selling, general and administrative expenses of $1,696,000 for the third quarter
were higher by 65% compared to the corresponding year-ago period and higher by
15% compared to the second quarter of fiscal 1997. As a percent of sales,
selling, general and administrative expenses were 24% of revenues in the current
quarter compared to 22% of revenues for the corresponding year-ago period and
the second quarter of fiscal year 1997. This increase in the ratio of SG&A
expenses to sales in the third quarter of fiscal 1997 versus the year-ago period
and the second quarter of fiscal 1997 is primarily the result of increased sales
and marketing expenses.

Company-funded research and development expenses of $538,000 for the third
quarter were higher by $425,000 (376%) compared to the year-ago quarter and
higher by $188,000 (54%) compared to the second quarter of fiscal year 1997.
This increase is an intentional result of the Company's growing commitment to
internally-funded research and development programs.

The Company produced a net profit of $503,000 during the third quarter. This is
an improvement of $251,000 (100%) over net profit in the year-ago quarter and an
improvement of $52,000 (12%) over the net profit reported in the second quarter
of fiscal 1997. The improved profitability results primarily from increased
sales volume and reduced costs of sales and contracts as a percentage of
revenue, partially offset by higher selling, general and administrative expenses
and Company-funded research and development.



                                       -8

<PAGE>   9



                     AMERICAN SCIENCE AND ENGINEERING, INC.
           ITEM 2 - MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                       CONDITION AND RESULTS OF OPERATIONS
                                   (Continued)


Liquidity and Capital Resources
-------------------------------
Net cash used by operating activities during the first nine months of fiscal
year 1997 was $922,000, compared to $975,000 net cash used during the
corresponding year-ago period. Cash and cash equivalents decreased by $1,262,000
to $2,115,000 as of December 27, 1996, compared to $3,377,000 on March 29, 1996.
This decrease is largely the result of normal drawdowns on unrestricted customer
cash advances for certain projects-in-progress. Working capital increased by
$1,682,000 (25%) since March 29, 1996, growing from $6,810,000 to $8,492,000 at
the end of the third quarter.

No external borrowings were outstanding at the end of either the current or
previous quarter. Management believes the Company has access to sufficient
capital resources to support operations over the next several quarters.


                                       -9

<PAGE>   10


                     AMERICAN SCIENCE AND ENGINEERING, INC.

Part II  - Other Information

Item 1.  Legal Proceedings
In the Company's lawsuit against Martin Annis and AnnisTech, Inc., the
Massachusetts Superior Court issued a preliminary injunction prohibiting Dr.
Annis and AnnisTech from using AS&E's trade secrets or proprietary technology
and from working on a particular government contract. The injunction was upheld
by a single justice of the Massachusetts Appeals Court and remains in effect as
of the date of this filing.


Item 6.  Exhibits and Reports on Form 8-K
         --------------------------------
              (a)   Exhibit Index
                    -------------
                    Exhibit                                            Page
                    -------                                            ----
                    (11)    Statement re: Computation                    6
                            of Income per Common and
                            Common Equivalent Share

              (b)   Reports on Form 8-K
                    -------------------
                    No reports on Form 8-K were filed during the quarter.


SIGNATURES
----------
Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this Report to be signed on its behalf by the
undersigned hereunto duly authorized.

                                   AMERICAN SCIENCE AND ENGINEERING, INC.
                                   (Registrant)



Date: 3 February 1997              __________________________________________
                                   Lee C. Steele
                                   Vice President and Chief Financial Officer


Safe Harbor Statement
---------------------
The foregoing 10-Q contains statements concerning the Company's financial
performance and business operations which may be considered "forward-looking"
under applicable securities laws.

The Company wishes to caution readers of this Form 10-Q that actual results
might differ materially from those projected in any forwardlooking statements.

Factors which might cause actual results to differ materially from those
projected in the forward-looking statements contained herein include the
following: Significant reductions or delays in procurements of the Company's
systems by the United States Government; disruption in the supply of any
sole-source component incorporated into the Company's products (of which there
are several); litigation seeking to restrict the use of intellectual property
used by the Company; potential product liability claims against the Company;
global political trends and events which affect public perception of the threat
presented by drugs, explosives and other contraband; the ability of governments
and private organizations to fund purchases of the Company's products to address
such threats; and the potential insufficiency of Company resources, including
human resources, capital, plant and equipment and management systems, to
accommodate any future growth. These and certain other factors which might cause
actual results to differ materially from those projected are more fully set
forth under the caption "Risk Factors" in the Company's Registration Statement
on Form S-3 (SEC File No. 333-9151).

                                       -10