As part of the Research and Development phase of the Uranium Mill Tailings Remedial Action (UMTRA) program, the Lawrence Berkeley Laboratory (LBL) has set itself the goal of explaining the physico-chemical evolution of the Riverton site on the basis of the already collected field data at the site (Tokunaga and Narasimhan, 1982, Smith and Moed, 1982; White et al., 1984). The predictive aspects as well as addressing the question of critical quantity of field data have to be considered during the design phase of the project as a joint effort between the LBL team and the construction engineers. At the present time, LBL is in the process of completing the Research and Development phase of the work. As of this writing, the development of an appropriate set of mathematical models has been completed. The computations of the soil-water regime at the upper tailings surface, involving climatological factors is nearing completion. Computations of chemical transport are still in progress. This paper is devoted to a description of the key mathematical issues, the mathematical models that are needed to address these issues and a discussion of the model results pertaining to the soil water regime at the tailings-atmosphere interface. 11 references, 3 …