A rigorous modal expansion analysis is presented for a monopole antenna fed through an infinite perfectly conducting ground plane by a coaxial transmission line. An infinite perfectly conducting plate is introduced to facilitate the use of the modal expansion method. The surface current and input impedance of the monopole antenna result from finding the expansion coefficients of the electromagnetic field expressions by enforcing boundary conditions at conducting surfaces and regional interfaces. Numerical results for the current distribution and input admittance of a parallel plate antenna and a monopole fed by a coaxial line are presented and compared with available data in the literature. Very good agreement is observed. Also examined is the effect of the junction between the feed line and the monopole on the antenna's admittance.