Abstract Modal analysis in finite element packages gives natural frequencies and mode shapes, but not modal damping values. Given a constitutive relation for specific material dissipation, volume integrals of the per cycle dissipation can be used to estimate the modal damping. Here, we adopt a well known power law model for such specific dissipation. We develop a modal damping estimation procedure for thin-walled components using shell elements in a commercial finite element package. We validate our shell element results against both analytical results and a solid elements approach developed elsewhere. Our computational approach allows complex geometries in a study of the effects of shape on damping. Finally, we demonstrate the efficacy of both stress concentrations and small tuned resonant appendages in increasing damping.