We discuss here numerical modeling of active media of a nuclear-pumped laser in the mixture of He-Cd-CCl4 (325.0 nm) using a detailed nonstationary kinetic model. The mechanisms have been studied of the effect of CCl4 admixture on the relaxation processes in He-Cd plasma as well as on the lasing process. The influence that may exhibit addition of nitrogen on laser emission characteristics has been studied as well. It is shown that among the main factors that may prevent lasing at the transition with the wavelength of 325.0 nm there are parasitic absorption of the laser emission by cadmium atoms in metastable states and capture of the pump by minor, uncontrolled, admixtures as water vapor, nitrogen, and so on. The modeling made enabled us to deduce optimal conditions for Cd-lasers operation when pumped with a pulsed reactor of BARS-6 type.