**Exhibit 31.2**

**CERTIFICATION OFCHIEF FINANCIAL OFFICERSection 302 Certification**

I, Kenneth J.Galaznik, certify that:

1.                 I have reviewedthis annual report on Form 10-K of American Science and Engineering, Inc.;

2.                 Based on myknowledge, this report does not contain any untrue statement of a material factor omit to state a material fact necessary to make the statements made, inlight of the circumstances under which such statements were made, notmisleading with respect to the period covered by this report;

3.                 Based on myknowledge, the financial statements, and other financial information includedin this report, fairly present in all material respects the financialcondition, results of operations and cash flows of the registrant as of, andfor, the periods presented in this report;

4.                 The registrant’sother certifying officer and I are responsible for establishing and maintainingdisclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and15d-15(e)) and internal control over financial reporting (as defined inExchange Act Rules 13a-15(f) and 15d-15(f)) for theregistrant and have:

a)               Designed suchdisclosure controls and procedures, or caused such disclosure controls andprocedures to be designed under our supervision to ensure that materialinformation relating to the registrant, including its consolidated subsidiary,is made known to us by others within those entities, particularly during theperiod in which this annual report is being prepared;

b)              Designed suchinternal control over financial reporting, or caused such internal control overfinancial reporting to be designed under our supervision, to provide reasonableassurance regarding the reliability of financial reporting and the preparationof financial statements for external purposes in accordance with generallyaccepted accounting principles;

c)               Evaluated theeffectiveness of the registrant’s disclosure controls and procedures andpresented in this report our conclusions about the effectiveness of thedisclosure controls and procedures, as of the end of the period covered by thisreport based on such evaluation; and

d)              Disclosed in thisreport any change in the registrant’s internal control over financial reportingthat occurred during the registrant’s fourth fiscal quarter that has materiallyaffected, or is reasonably likely to materially affect, the registrant’sinternal control over financial reporting; and;

5.                 The registrant’sother certifying officer and I have disclosed, based on our most recentevaluation of internal control over financial reporting, to the registrant’sauditors and the audit committee of the registrant’s board of directors (orpersons performing the equivalent functions):

a)               All significantdeficiencies and material weaknesses in the design or operation of internalcontrol over financial reporting which are reasonably likely to adverselyaffect the registrant’s ability to record, process, summarize and reportfinancial information; and

b)              Anyfraud, whether or not material, that involves management or other employees whohave a significant role in the registrant’s internal control over financialreporting.
| Date: June 9, 2006 |                                     |
|-------------------------|------------------------------------------|
|                    | /s/  KENNETH J. GALAZNIK                 |
|                    | Kenneth J.  Galaznik                     |
|                    | *Chief  Financial Officer and Treasurer* |

 

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