Cylindrical shells with discontinuity in the thickness and subjected to harmonic axisymmetric load are analyzed for a clamped-free end condition. The loadings 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 method is used for the analysis. A thin shell finite element with four degrees of freedom per node and two nodes per element 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 the first three modes and for various step-ratios in the thickness. The weight of the shell is kept constant for various step-ratios. It is shown that the maximum displacement and maximum stress decreases for certain types of thickness variations. © 1995.