The usage of radioactive substances in science, industry, medicine and nuclear power plants is generating radioactive waste. The only way we can effectively protect ourselves from their deleterious effects is by appropriate waste disposal. In order to secure long-term safety of the disposal facilities, we have to understand the transport mechanisms in porous materials. We can then use mathematical models to describe the underground currents and possible transportation routes of radionuclides from the
disposal facilities through geological formations. Theoretical part of the thesis contains the description of physical principles of radioactivity, classification system of radioactive waste and disposal possibilities for low-level and intermediate waste with information on type and quantity of radioactive waste in Slovenia. Theoretical basis of groundwater flow and related phenomena of flow in porous materials is also described. Experimental part describes the making of mathematical models for disposal facilities, that deal with low and intermediate level waste (LILW). First model describes the disposal of LILW without cover, the second describes the disposal of LILW with cover layer. The results were summarized and indicate the influence of cover on groundwater flow through hazardous waste dump and transportation of radionuclides of Caesium (137Cs) and Iodine (129I). Models and calculations were made with HYDRUS- 1D software.