  We consider cloaking by a coated cylindrical system using plasmonic
resonance, and extend previous quasistatic treatments to include the effect of
finite wavelength. We show that a probe cylinder can still be cloaked at finite
wavelengths, but the cloaking cylinder develops a non-zero scattering
cross-section. We show that this latter effect is dominated by a monopole term
in the case of an ideal (lossless) cloaking material, and by a dipole term in
the case of a realistic (lossy) material. It can be reduced but not eliminated
by variations of geometric or dielectric parameters of the cloaking cylinder.
