A perfectly conducting, infinitely long cylindrical wire of radiusasurrounded by an insulating layer of a cylindrical sheath of free space of radiusbis immersed in a homogeneous, warm plasma of infinite extent. Using the linearised plasma theory and approximate boundary conditions, the dispersion equation for the propagation coefficient along the wire is derived. The numerical solution of the dispersion equation for a wide range of values for the radius of the cylindrical wire and the width of the insulating sheath shows that the propagation coefficient along the cylindrical wire is close to that of the plasma mode in an unbounded plasma, in the frequency range for which the electromagnetic and the plasma space waves are excited, that is for frequencies above the plasma frequency. It is therefore concluded that, for a finite antenna immersed in a warm plasma without or with an insulating sheath, it is appropriate to include in the approximation for the current distribution along the antenna a part which has the propagation coefficient of the order of magnitude of the plasma wave.