In this paper we consider the problem of the dominant mode scattering by a layered circular cylindrical post in a rectangular waveguide. Both waveguide filter synthesis procedures and measurements of complex dielectric permittivity of materials require a solution to the inverse scattering problem. Since the computation time of an algorithm for solving the inverse scattering problem depends directly upon computation time of an algorithm for the forward scattering problem, our goal is to find an approach that provides both sufficient accuracy of results and rapid convergence. Over the last several decades, a number of approaches have appeared proposed by various authors for solving problems of scattering by a cylindrical post in a rectangular waveguide. The approach presented in this paper is a modified version of one of those approaches that provides sufficiently rapid convergence and results with a reasonable degree of accuracy. This modification allows a solution to the problem of scattering by a layered post. The approach divides the waveguide into separate regions by introducing imaginary cylindrical surface. In the outer regions the electromagnetic field is represented in terms of infinite series of rectangular waveguide modes. In the central region as well as in the layers of post, the field is represented in terms of cylindrical waves. By applying the point-matching method at the imaginary cylindrical surface and truncation of infinite series, a system of linear algebraic equations is obtained.