The work was carried out within the framework of the cascade-probabilistic method, the essence of which is to obtain and further apply cascade-probabilistic functions. The obtained models make it possible to trace the entire process in development and in the future can be used in industry to obtain materials with predetermined characteristics. The results of the obtained studies can also be used by specialists in the field of solid-state radiation physics, in сosmophysics. The cascade-probability functions, the energy spectra of primary knocked-on atoms (PKA), and the concentration of vacancy clusters in molybdenum irradiated with alpha particles were simulated. Some of their properties and patterns were established. Methods of mathematical analysis, probability theory, and numerical methods were used in the research process.