Two fundamental concerns must be addressed when attempting to isolate low-level waste in a disposal facility on land. The first concern is isolating the waste from water, or hydrologic isolation. The second is preventing movement of the radionuclides out of the disposal facility, or radionuclide migration. Particularly, we have investigated here the latter modified scenario.To assess the safety for disposal of radioactive waste-concrete composition, the leakage of 137Cs from a waste composite into a surrounding fluid has been studied. Leakage tests were carried out by original method, developed in Vinca Institute [1,2,3,4,5]. Transport phenomena involved in the leaching of a radioactive material from a cement composite matrix are investigated using three methods based on theoretical equations [6,10]. These are: the diffusion equation for a plane source an equation for diffusion coupled to a first-order equation, and an empirical method employing a polynomial equation‥ The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choises for radioactive waste packaging for a future Serbian radioactive waste disposal center.