This work is focused on numerical modeling of an ArF* laser operating on the Electra electron beam (e-beam) facility at the Naval Research Laboratory. The results are based on a suite of codes that includes electron kinetics derived from the electron Boltzmann equation, plasma chemistry, lasing amplification, and 3-D radiation transport. The mechanisms of formation and destruction of ArF* molecules have been investigated. Time-dependent laser parameters, such as small signal gain, nonsaturable absorption, saturation intensity, and amplified spontaneous emission (ASE) and their dependence on e-beam power deposition in the range of 0.5-1 MW/cm(3), gas pressure of 0.8-1.4 atm, and F-2 concentration of 0.1%-3.0%, are investigated. The modeling results show that the ArF* laser is an efficient and coherent light source at 193 nm ultraviolet wavelength.