In this paper the derivation of a rigorous expression of the input admittance of a coaxially fed, infinite, lossy parallel plate waveguide (PPWG) is presented. The derivation makes use of the dyadic Green's function of the PPWG expressed as series a cylindrical wave-functions. Losses into the dielectric plates and on the conductors are considered rigorously. The approximation used in results presented in the past literature are critically discussed. Numerical experiments are performed to show the effects of the finite conductivity on the input impedance of the PPWG.