The aim of this paper is to describe a finite element method used to investigate the contact stresses due to a combination of normal and tangential forces in coating-substrate systems. The stresses have been computed for various values of the coating-to-substrate Young's modulus ratio, friction coefficient and coating thickness. Results of simulations showed that the influence of coating thickness on the stresses (at the surface and the interface) was as important as coating-to-substrate Young's modulus ratio was high. The magnitude of von Mises stress and the location of its maximum depend strongly on both friction coefficient and coating-to-substrate Young's modulus ratio.