In this study, a method has been developed in order to calculate the subsurface contact stresses in a functionally graded coating loaded by a frictional flat stamp on the contact surface. Plane elasticity is considered; Poisson's ratio is taken to be constant for the FGM coating and the substrate is taken to be homogeneous. The problem is reduced to a singular integral equation which is solved numerically by means of an expansion collocation technique. The series expansions utilized in the solution of the singular integral equation are expressed in terms of Jacobi polynomials. Effects of punch length, punch location, coefficient of friction and material properties on the subsurface stresses are investigated.