A contact mechanics analysis of interfacial delamination in elastic and elastic-plastic homogeneous and layered half-spaces due to normal and shear surface tractions induced by indentation and sliding was performed using the finite element method. Surface separation at the delamination interface was controlled by a surface-based cohesive zone constitutive law. The instigation of interfacial delamination was determined by the critical separation distance of interface node pairs in mixed-mode loading based on a damage initiation criterion exemplified by a quadratic relation of the interfacial normal and shear tractions. Stiffness degradation was characterized by a linear relation of the interface cohesive strength and a scalar degradation parameter, which depended on the effective separation distances corresponding to the critical effective cohesive strength and the fully degraded stiffness, defined by a mixed-mode loading critical fracture energy criterion. Numerical solutions of the delamination profiles, the subsurface stress field, and the development of plasticity illuminated the effects of indentation depth and sliding distance on interfacial delamination in half-spaces with different elastic-plastic properties, interfacial cohesive strength, and layer thickness. Simulations yielded insight into the layer and substrate material property mismatch on interfacial delamination. A notable contribution of the present study is the establishment of a computational mechanics methodology for developing plasticity-induced cumulative damage models for multilayered structures.