Contact stress distribution at an FGM surface is evaluated using an analytical technique based on the singular integral equations. An FGM half-plane is assumed to be in sliding contact with a rigid stamp of an arbitrary profile. The functionally graded medium is assumed to possess two-dimensional material property variations. Two independent nonhomogeneity constants are used to derive the governing partial differential equations. By using the integral transform techniques, all boundary conditions are satisfied analytically and the problem is reduced to a singular integral equation. The integral equation is solved numerically by adopting an expansion-collocation scheme. Presented numerical results consist of contact pressure distributions at the FGM surface as functions of nonhomogenity parameters and coefficient of friction.