Functionally graded materials have been taken into consideration by many researchers in the last two decades. Gradual changes of mechanical properties in FGMs decrease stress concentration, crack initiation and propagation and delamination. Many of the present and potential applications of FGM contain contact loading.This kind of loading causes surface crack initiation which is followed by subcritical crack propagation.Thus, propagation of surface cracks is one of the most important failure mechanisms in FG structures. In this article two dimensional sliding contact of a rigid flat punch on a homogeneous substrate with an FGM coating is studied. Plane strain condition is considered in this problem. The Properties of the substrate and the FGM layer are assumed to be elastic and the Poisson’s ratio is assumed to be constant. The modulus of elasticity in the graded layer is calculated based on TTO model approximation. This model defines a parameter q which considers the microstructural interactions. The governing equations are solved by Finite Difference method by means of MATLAB software. The influence of different parameters such nonhomogeneity,q, the dimensions of the punch, the thickness of the graded layer and the coefficient of friction on the mode I and II stress intensify factors are investigated.