This study investigates the plane frictional contact problem of a cylindrical punch on a functionally graded orthotropic medium (FGOM). Both analytical and computational methods are developed to obtain the contact stresses. The elastic modulus is assumed to vary exponentially and the principal axes of orthotropy are assumed to be aligned with the global coordinates. In the analytical formulation, plane elasticity equations are converted to Cauchy-type singular integral equation of the second type by using Fourier Transform technique. The resulting integral equations are then solved numerically to obtain the contact stresses throughout the medium for plane stress condition. In the computational model, the elastic modulus of each finite element is specified at its centroid by using the predefined.functional variation. The results obtained from the finite element analysis is verified by comparing the results obtained using the analytical formulation. The results of this study can guide tribology engineers in determining the contact stresses that have a great effect on the wear resistance of mating components.