Analyzing the yielding behavior of the contacting pairs is very important to determine the crack initiation, propagation and failure at different interfaces. In the present study, yielding behavior based on von Mises stress criterion is investigated for different systems including single layer, double layer and functionally graded material layer where stress distribution, elastic modulus and yield strength play vital rule. Here, for the analysis Finite Element software ABAQUS 6.14-2 is used to solve contact problem and to determine the yielding inception on the surface, inside the coating or the substrate for different input parameters at the contact. Intel Fortran Compiler XE 2013 along with Visual Studio 2012 are used for introducing the mechanical property through coding for functionally graded materials. This problem is modeled as a rigid sphere indenting half space deformable body. Upon verification and validation of the model with various published configurations, a parametric study is carried out for different conditions including various loadings, coating thicknesses and different elastic-plastic material properties to understand the yielding behaviors of the coating/substrate system and to find optimize values for the best resistance to failure.