Development of high-energy nuclear-pumped lasers is still a challenging and actual, but not yet implemented task of the joint application of two high technologies: nuclear and laser. Experimental studies are extremely cost-based and unsafe. It balks greatly the progress in this research area. The detailed kinetic models of nuclear-exited plasma can significantly accelerate the development of high-energy nuclear-pumped lasers. The authors developed a unique multi-component kinetic model of helium-nitrogen-hydrogen active medium excited by uranium fission fragments, which takes into account all the major processes of selective check-working laser levels. It was ascertained by the methods of mathematical modeling that the upper laser level population is defined almost equally both by the charge exchange processes of atomic and molecular helium ions in collisions with nitrogen molecules and by the Penning processes at molecular nitrogen collision with the excited helium atoms. Considering the fact that in typical conditions of nuclear pumping the helium-nitrogen-hydrogen active laser medium excited by fission fragments is strongly inhomogeneous, the mathematical modeling data were analyzed. Under real nuclear pumping medium experiment the power gain coefficient of laser beam per a pass does not differ greatly both when taking into account the inhomogeneous energy input distribution to the active medium, and when replacing it by the uniform one. At this time the instant total energy input into the active medium must be the same. These differences can be approximately taken into account by introducing an effective linear loss factor b?, which is10-5 cm-1 according to the calculations of the research.