Abstract: In order to solve the problem of electromagnetic, scattering by a dielectric-coated conducting circular cylinder, the total field excited by an electric and amagnetic dipoles exterior to the cylinder is derived in terms of dyadic Green's function (DGF) technique. Then, the scattering problem can ko solved on basis of the relation between the total and the scattered, field. The solution of the scattorod field can be obtained directly from the general formula of the scattered field as the cylinder is illuminated by a spherical wave. For a plane wave of arbitrary polarization incident to the cylinder from the direction (θ₀, φ₀), the scattered field can be given by the solution of the scattered field with a spherical wave incident as the center of the spherical wave moves to infinity, For an astigmatic wave incident to the cylinder, the scattered field can be derived by suporposing or integrating of the scattered field with the special spherical wave incident.