In this paper, the radiation from a circular cylindrical monopole fed through a perfectly conducting ground plane by a coaxial transmission line is analyzed using the method of auxiliary sources. The proposed method is applied by introducing a set of fictitious sources aligned with the monopole's axis for the direct description of the radiated electromagnetic field above the ground plane, under the assumption of a single transverse electromagnetic mode existing in the annular aperture of the line. The currents of the fictitious sources are derived by imposing the continuity condition of the tangential electric field on the physical surface of the dipole. For the occasion, the fictitious sources are chosen to be spatially overlapped sinusoidal dipoles. It is substantiated that this choice results in a noteworthy acceleration of the convergence rate of the solution in comparison with the one associated with infinitesimal dipoles, which are usually used in current-model-based techniques. Since the currents of the fictitious sources are determined, pertinent quantities of great interest, including the current distribution along the monopole, the input impedance/admittance, and the field intensities in the near and the far region, can be determined in a straightforward manner. Several examples concerning various geometries are established and compared with previously published data.