Abstract Cantilever beams with discontinuity in the thickness and subjected to harmonic point load have been analyzed. A beam element with 2 DOF (degrees of freedom) per node is used for the analysis. Three beam models are analyzed for possible reduction of maximum displacement and maximum stress by choosing the discontinuity at different locations. Numerical results are presented for various step-ratios in the thickness for the first three modes. The weight of the beam is kept constant for various step-ratios. It has been shown that the maximum displacement and maximum stress decreases for a certain type of thickness variations presented in this paper.