Orthotropic cylindrical shells with discontinuity in thickness and subjected to asymmetric loading have been analyzed. A higher-order finite element based on thick shell theory is used for the analysis. The material used is a glass/epoxy composite with 0 ° and 90 ° fiber orientation with respect to the axial direction of the cylinder. The loadings considered are a line load along the length of the cylinder and a point load at the mid-section. Numerical results are presented for various end conditions and step-ratios in the thickness. The weight of the shell is kept constant for various step-ratios. It has been shown that a 90 ° fiber orientation gives smaller deformations and stresses for asymmetric loading than a 0 ° fiber orientation. The variation in the thickness reduces the maximum stresses up to a certain step-ratio for various end conditions presented in this paper. © 1994.