A detailed study has been conducted on the effect of different types of variations of thickness profiles on the amplitudes of deflection and the dynamic bending stress of a cantilever beam under a point harmonic load. The response has been calculated for excitation frequencies corresponding to the first three natural frequencies. In each case the results obtained for different types of thickness variations are compared with those obtained for a uniform thickness beam. It is observed that considerable reduction in amplitude and/or bending stress can be achieved by proper selection of thickness variation. © 1994 Academic Press Ltd.