Abstract Finite element techniques are used to calculate the stress concentrations near the free edge and along the interface of thin films which are bonded to stiff substrates. The material of the film is modeled as elastic-plastic with a linear power-law hardening stress-strain curve in simple shear. It is assumed that the film material is characterized by J 2 deformation theory, and that far from the free edges the film is in a state of uniform balanced biaxial stress which may be due to misfit strain, to thermal strain or to intrinsic stress. Emphasis is placed on the stress concentrations in films of small aspect ratio (modeling the early stages of island growth) or of large aspect ratio (modeling epitaxial or layer-by-layer growth) and on the effect of the hardening exponent on the resulting stress concentrations. It is found that stress concentrations are localized near the film-substrate interface, that films of small aspect ratio have smaller stress concentrations than films of large aspect ratio, and that plastic deformation significantly reduces the stress levels near the interface, although close to the free edge the stress levels are still higher than the far field uniform stresses.