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The scattering of an electromagnetic wave from a conducting cylinder clad with an anisotropic plasma of arbitrary electron density is considered, and the eigenfunction solution is obtained. The resonant behavior of the system is investigated. The resonant conditions are obtained, and damping of the resonant scattering by finite size effects and collisional dissipation is studied. The Rayleigh and geometrical optics limiting cases are derived, and the approach of the plasma scattering to that from a metallic body for increasing plasma frequency (electron density) is obtained. Comparisons with the scattering from an unclad cylinder and from a planar conductor sheathed with a plasma are made.