We present a full-wave numerical tool for the simulation of plasma antennas. The tool makes use of a hybrid formulation that allows treating the plasma with a Finite Element discretization, and the metallic parts with the Method of Moments. The finite element discretization is solved using a state-of-the-art sparse solver (MUMPS) in order to reduce the computational time at a minimum. The accuracy of the tool is tested by comparing the results obtained with it against those obtained with a benchmark code. Finally, a novel dual-mode plasma antenna is designed using the aforementioned tool.