This paper focuses on the electromagnetic backscattering from a finite-length rectangular trough in a flat plate of finite dimension. Based on the method of dyadic Green's functions and geometrical theory of diffraction (GTD), the magnetic field integrated functions (MFIF) of this problem are obtained. The physical basis formulation, as introduced by Richmond (see IEEE Trans. Antennas and Propagation, vol.33, p64-8, 1985), is used to express the unknown currents in the trough aperture, and the Galerkin solution is used to compute the MFIF. Finally the RCS of such a trough is computed, and some plots are obtained and compared.