A hybrid modal solution is developed for the circular semi-infinite dielectric rod antenna excited in the HE_{11} hybrid mode. Numerical results for the near-zone and far-zone fields, as well as the gain, beamwidth, and percentage of power radiated, are determined for three rods of different diameter and dielectric constant by enclosing the rods with a concentric metal pipe and allowing the radius of the pipe to become large. Comparison is made between these results and previous approximate methods of solution that have been applied to the dielectric rod antenna.