This paper presents simulation results for a microwave (2.45 GHz) plasma reactor, operated by an axial injection torch (AIT). The study gives a two-dimensional description of the AIT-reactor system, based on an electromagnetic model (that solves Maxwell's equations adopting a time-harmonic description, yielding the distribution of the electromagnetic fields and the average power absorbed by the plasma), and a hydrodynamic model (that solves the Navier-Stokes' equations for the flowing neutral gas, yielding the distribution of mass density, pressure, temperature, and velocities). Comparison between model results and experimental measurements reveal common variation trends, with changes in the reactor height, for the power reflected by the system, and yield a qualitative agreement for the axial profile of the gas rotational temperature. Model results, such as the power transmission coefficient and the gas temperature, are particularly dependent on the reactor dimensions, the electron density and temperature, and the gas input flow, which indicates that simulations can be used to provide general guidelines for device optimization.