The use of uranium nanoparticles dispersed in a laser-active medium instead of traditionally used methods of heterogeneous nuclear pumping of active gas medium can increase the fraction of energy carried by fission fragments from the condensed phase into the gas medium by more than an order of magnitude. This creates the conditions for increasing the efficiency of nuclear into optical radiation energy conversion. However, the scattering and absorption of laser radiation by an active medium containing uranium nanoparticles are important factors preventing the laser radiation generation in such a medium. Mathematical modeling of the generation and amplification of laser radiation in a moving spatially inhomogeneous nuclear-excited neutron-irradiated argon-xenon medium containing uranium nanoparticles injected into a cylindrical laser-active dusty element, taking into account optical inhomogeneities caused by the dust component. The process of amplification and intensity distribution of a master oscillator laser beam in a moving spatially inhomogeneous nuclear-excited argon-xenon neutron-irradiated medium containing uranium nanoparticles has been studied for the first time. Data were also obtained on the propagation of a light beam near a relatively sharp dust component concentration decrease in moving gas medium. As a brief result: moving spatially inhomogeneous nuclear-excited neutron-irradiated argon-xenon medium containing uranium nanoparticles does not have a pronounced destructive effect on the propagation of laser radiation in it, on condition that the light flux is not wider than the dust component.