We have modeled the properties of a transverse electron beam pumped argon ion laser using Monte Carlo techniques. We studied the lasing transitions at 4765 and 4880 A˚ for electron energies up to 300 eV, for conditions of pressure and degree of ionization similar to those employed in conventional lasers. We find lasing efficiencies to be comparable to those in the conventional axial discharge argon ion laser. However, it may be possible to attain higher efficiencies if much higher degrees of ionization can be reached.