We apply the effective medium theory combined with the conventional periodic method of moments (MoM) to analyze frequency selective surfaces (FSSs) on periodic and anisotropic substrates. Based on the effective medium theory, even periodic and anisotropic substrates can be considered homogeneous; thus, the Green's function can be obtained. The resulting integral equation can then be solved by the MoM using rooftop basis functions and Galerkin testing functions. We analyze an example using this technique, and the numerical results agree with Fallahi's full-vector semi-analytical method, showing an increasing difference between the results as the frequencies increase. These results show that the proposed method is effective for analyzing FSSs on periodic and anisotropic substrates.