A fast method to solve contact problems when one of the mating bodies contains multiple cubical heterogeneities is proposed in order to deal with non-uniform elastic-plastic coatings. Numerical results are presented for soft or hard coatings, and various cases are considered. Elementary solutions are still fully analytical, using the Eshelby's equivalent inclusion method so the computing time and allocated memory are kept small, compared to the finite element method. An iterative process is implemented to determine the displacements and stress fields caused by the eigenstrains of all heterogeneities. The proposed method can be seen as an enrichment technique for which the effect of heterogeneities is superimposed to the homogeneous solution in the contact algorithm. 3D and 2D FFT are utilized to improve the computation efficiency. Uniform as well as non-uniform coating thickness can be treated by this method.