The von Mises stress distributions in a hard coating and in elastic sliding contact are analysed by the finite element method. An elliptical distribution of normal and traction contact pressure is assumed for the analysis of von Mises stress for various combinations of coating thickness, friction coefficient and elastic modulus of the coating and substrate. The position of yield is found with the calculated result and the local yield map is introduced in relation to the yield strength ratio of the coating to the substrate and the ratio of the coating thickness to the half-contact width. The local yield maps show that yield at the coating substrate interface in the substrate is the most general case under a wide range of contact conditions. An interface yield map for identification of the yield regime and the no-yield regime at the coating-substrate interface in the substrate is introduced in relation to the normalized critical maximum contact pressure and the ratio of the coating thickness to the half-contact width, and a sample equation is introduced for the calculation of the critical maximum contact pressure for the yield at the coating substrate interface in the substrate based on the map.