The scattering problem by metallic gratings has become one of fundamental problems in electromagnetics. In this paper, a thin metallic grating placed in conical mounting is treated as a lossy dielectric grating expressed by complex permittivity and thickness. The solution of the metallic grating by using the matrix eigenvalue calculations is compared with that of the plane grating by using the resistive boundary condition and the spectral Galerkin procedure, and the availability of the resistive boundary condition for thin metallic gratings in conical mounting is investigated. In order to improve the convergence of the solutions of thin metallic gratings, the spatial harmonics of flux densities which are continuous function instead of electromagnetic fields are used.