A detailed study has been conducted on the effects of different types of variations in profile and thickness on the amplitude of deflection and the dynamic of a cantilever beam subjected to a harmonic end moment. The response has been calculated for the first four modes of vibration. 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 deflection and/or bending stress can be achieved by proper selection of the thickness variation. © 1995 Academic Press Ltd.