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The paper presents a novel approach for the analysis of multilayer frequency selective surfaces, consisting of either multiple grids perforated periodically with holes, or a metal screen perforated with stepped apertures. This approach is based on the segmentation technique and the MoM/BI-RME (method of moments/boundary integral-resonant mode expansion) method. In fact, by using the segmentation techniques, these components can be reduced to cascaded waveguide step discontinuities, either between a metallic waveguide and a waveguide with periodic boundary condition or between two metallic waveguides. Both types of discontinuities are considered and are analyzed by the MoM/BI-RME method. Some examples are also reported.