In order to avoid micro-crack initiation at the interface between a coating and a substrate under sliding contact, one of the methods is to design an interlayer to prevent the local yield, because micro-crack initiates usually from the local yield. In this paper, the finite element method was used to calculate the distribution of maximum von Mises stresses in a hard coating with an interlayer. The effect of the interlayer on the position of local yield was cleared by comparing the maximum von Mises stresses with the yield strength of materials. As a result, the local yield map for identification of the yield position was introduced with three parameters, i.e. the ratio of yield strength of the interlayer to the top coating; the ratio of the top coating thickness to the half contact width; and the friction coefficient. The local yield maps show that when the friction coefficient is smaller than 0.25, yield occurs in the interlayer within the range of (Y-inter/Y-top) <0.5 and in the substrate within the range of (Y-inter/Y-top) >0.5. When the friction coefficient is larger than 0.5, yield occurs on the surface within the range of (Y-inter/Y-top) >0.5. Here, Y-inter, is the yield strength of the interlayer and Y-top is the yield strength of the top coating.