The world’s sustainable development of nuclear power engineering during last decades resulted in large number of radioactive wastes. Currently, each state having nuclear power engineering systems in possession, utilizes the concept of geological disposal as a long-term strategy of radioactive wastes treatment that requires continuous advancements in methods and means due to wastes and standards of radiation monitoring stringency. The article considers the features of radioactive substance content dynamics simulation for single- and multi-walled solid radioactive waste stores, being the product of uranium production, represented by one-dimensional equations and the second and first order sets of equations. The potentials of the existing models, that take into account complex interactions between radionuclides and environment along with possible sources of pollution and mechanisms of radioactive substance transfer, were reviewed. The data availability of temporary radionuclide content evolution inside the store to assess possible effect on environment and people based on the results of mathematical modelling of the considered numerical expressions was emphasized. It was shown, that current models allow analysing and predicting transfer of radionuclide solutions and other substances due to finding solution to contemporary scientific engineering and environmental problems. It was noted, that nowadays there is no model providing forecast of radionuclide content spatial and temporal variations within various store layers to study the accumulated radioactive wastes revealing the mechanisms of their formation, to analyse the features of their distribution, to determine the areas of their active concentration and to define the radionuclide migration activity during storage.