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In this paper, based on the formulation of the Kobayashi and Nomura method, EM plane wave scattering by a material loaded trough on a ground plane is approximately analyzed by applying the simplest standard impedance boundary condition (SIBC). We adapted the SIBC to the eigen-function expansion. We have already presented the H polarization case in Sato and Shirai (1998). So the formulation is extended and derived here for the E polarization case. In order to check the validity of this approximation, numerical calculations have been done for various parameters. Differences between the E and H polarizations have been also discussed.