Numerical analysis of functionally graded material (FGM) coated surface in two-dimensional frictional contact with arbitrary shaped rigid stamp is presented. Loads are applied such that the stamp is fully sliding. Pressure distribution at the interface for arbitrary profile is expressed as a modified cosine series. Due to its ability to analyze arbitrary shaped contacts, it can be a powerful design tool for evaluating contact response due to different shapes and sizes of indenter. A multi-layer model of FGM coating with piecewise constant approximation for Young's modulus variation is used. Simplifications have been suggested in the formulation to aid numerical evaluation of the resulting integrals. The method is demonstrated for symmetric and unsymmetric profiles and compared with results from literature. © 2016 Elsevier Ltd