Cylindrical shells with a discontinuity in the thickness and subjected to axisymmetric impulse load have been analyzed. The loadings considered are a uniform internal pressure and a circular ring load at the mid-section. A 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 to indicate possible reductions of maximum displacements and maximum dynamic stresses by choosing the discontinuity at different locations. Numerical results are presented for clamped-clamped boundary conditions and for various step-ratios in the thickness. The weight of the shell is kept constant for the various step-ratios. It is shown that the maximum displacements and maximum dynamic stresses decrease for a certain type of thickness variation. © 1995 by Academic Press, Inc.