In this paper modelling of transverse vibration of a beam of linearly variable depth and constant thickness in the presence of an 'open' edge crack normal to its axis has been proposed using the concept of a rotational spring to represent the crack section and the Frobenius method to enable possible detection of location of the crack based on the measurement of natural frequencies. The method can also be used to solve the forward problem. A number of numerical examples are presented involving cantilever beams to show the effectiveness of the method for the inverse problem. The error in the prediction of crack location is less than 2% and size is around 10% for all locations except at the fixed end. Crack sizes 10-50% of section depth have been examined. (C) 1999 . .