A cylindrical antenna is embedded in a dielectric cylinder, which is surrounded by a compressible isotropic electron plasma. The antenna impedance is formulated variationally by considering the effects of surface waves supported by the antenna structure. The surface waves alter the antenna current distribution for frequencies near the plasma frequency, but their amplitude is decreased as the thickness of the antenna insulation increases. The antenna solution is verified by examining the electric surface fields excited by the approximated antenna current distributions, and the results are compared with other numerical solutions.