The influence of a constrained damping layer on the resonant response of orthotropic cylindrical shells to different types of loading is studied. The material damping in the composite facings is also accounted for in the analysis. Parametric studies are carried out using the finite element method for different core to facing thickness ratios, length to radius ratios and boundary conditions. The investigation is made not only with respect to the displacement response but also to the stress response. From the study it is found that inclusion of the damping layer is beneficial in reducing the resonant displacement and the stress magnitudes in composite shells. © 1995 Academic Press. All rights reserved.