Cylindrical shells with discontinuity in the thickness and subjected to harmonic axisymmetric loads 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 for possible reduction of maximum displacement and maximum stress by choosing the discontinuity at different locations. Numerical results are presented for clamped-clamped end conditions and for various step-ratios in the thickness, for the first three models. The weight of the shell is kept constant for the various step-ratios. It is shown that the maximum displacement and maximum stress decrease for certain types of thickness variations as presented in this paper. © 1995 by Academic Press, Inc.