In this paper, we describe a numerical method for determining the location of a crack in a beam of varying depth when the lowest three natural frequencies of the cracked beam are known. The crack is modelled as a rotational spring and graphs of spring sti!ness versus crack location are plotted for each natural frequency. The point of intersection of the three curves gives the location of the crack. Earlier work in this area involved the use of the Frobenius technique for solving the governing di!erential equation analytically and then using a semi-numerical approach to obtain the crack location. In this work, we use the "nite element approach to solve the same problem. The beam is modelled using beam elements and the inverse problem of "nding the spring sti!ness, given the natural frequency, is shown to be related to the problemof a rank-one modi"cation of an eigenvalue problem. Examples outlining the accuracy and ease of using this method are shown. The results are compared with those from semi-analytical approaches. The biggest advantage of this method is the generality in the approach; di!erent boundary conditions and variations in the depth of the beam can be easily modelled.