Cylindrical shells with discontinuity in the thickness and subjected to axisymmetric impulse loads have been analyzed. The impulse loads considered are uniform internal pressure and circular ring load at the tip. The semi-analytical finite element method is used for the analysis. A thin shell finite element with four degrees of freedom per node is used. Three shell models are analyzed for possible reduction of maximum displacements and maximum dynamic stresses by choosing the discontinuity at different locations. Numerical results are presented for clamped-free boundary condition and for various step-ratios in the thickness. The weight of the shell is kept constant for various step-ratios. It has been shown that the maximum displacements and maximum dynamic stresses decrease for certain types of thickness variations presented in this paper. © 1995.