A plane wave impinges on a perfectly conducting thick screen perforated with a periodic array of apertures with arbitrary cross-section. The transmission and reflection coefficients are determined by a mode matching technique, earlier used by other authors for the case where the apertures have the geometry of a classical waveguide. The fields outside the screen are expanded in Floquet modes, while the fields inside the apertures are expanded in waveguide modes, obtained by the finite element method (FEM). Excellent agreement between computed and measured transmission is found for a thick screen at the X-band (8.2-12.4 GHz). Moreover, the present method and the spectral Galerkin method (which assumes that the thickness of the screen is zero) is compared for very thin screens, e.g., for a frequency selective surface (FSS). Investigation of the thickness dependence is also done, and it is found that the bandwidth decreases when the thickness dependence is also done, and it is found that the bandwidth decreases when the thickness of the screen is increased. Finally two complex geometries, hexagonal and tripole apertures, are studied.