The shielding effectiveness (SE) of a metallic enclosure with double-layer frequency selective surface (DLFSS) has been calculated using a transmission line theory-based analytical formulation. The DLFSS layer placed on the front and back sides of the enclosure consists of a Greek cross aperture array. The equivalent circuit method and an empirical method are used to calculate the impedance of the Greek cross FSS. Then, the SE is calculated for various incidence and polarization angles. Calculated results are compared with the measured and numerical simulation results. © 2015 IEEE.