The general formulation of the environmental risk problem captures the entire process of identifying the source term of the risk agent, its fate and transport through porous media, estimation of human exposure, and conversion of such exposure into the risk level. The contaminant fate and transport is modeled using the solute flux formulation evaluated with its first two moments, which explicitly account for the spatial variability of the velocity field, sorption properties, and parametric uncertainty through the first-order analysis. The risk level is quantified on the basis of carcinogenicity using the risk factor (which describes the risk per unit dose or unit intake) employed to the total doses for individuals potentially consuming radionuclide-contaminated groundwater. As a result of the probabilistic formulation in the solute flux and uncertainty in the water intake and dose-response functions, the total risk level is expressed as a distribution rather than a single estimate. The results indicate that the geologic heterogeneity and uncertainty in the sorption estimate are the two most important factors for the risk evaluation from the physical and chemical processes, while the mean risk factor is a crucial parameter in the risk formulation. ¿ American Geophysical Union 1996