The problem of electromagnetic scattering, from a conducting cylinder of arbitrary cross-section covered by multiple layers of lossy dielectrics, is considered. The surface equivalence principle is used to reduce the problem to the solution of a set of coupled integral equations. The equations are then solved using the method of moments. Data are given for the surface currents, radiation patterns and scattering cross-sections for the case of TM incident waves. Computed results are in good agreement with exact and published data available.