The problem considered is an electrically thin dielectric insulating shell on an antenna composed of electrically thin circular cylindrical wires. The solution is a moment method solution and the insulating shell is modeled by equivalent volume polarization currents. These polarization currents are related in a simple manner to the surface charge density on the wire antenna. In this way the insulating shell causes no new unknowns to be introduced, and the size of the impedance matrix is the same as for the uninsulated wires. The insulation is accounted for entirely through a modification of the symmetric impedance matrix. This modification influences the current distribution, impedance, efficiency, field patterns, and scattering properties. The theory will be compared with measurement for dielectric coated antennas in air.