Based on the formulation of Kobayashi and Nomura's method (1957), electromagnetic plane wave scattering by a loaded trough on a ground is approximately analyzed by applying the standard impedance boundary condition (SIBC). Similar approximations using impedance boundary conditions have been reported previously by Barkeshli and Volakis (1990) and by Whites, Michielssen and Mittra (1993). While they applied the SIBC to the integral equation formulation, we adapted the SIBC to the eigen-function expansion in order to check the validity of the approximated solution derived, numerical calculations have been done for various parameters. The time harmonic factor e/sup -i/spl omega/t/ is assumed and suppressed throughout the context.