Assessment of the environmental fate and behavior of constituents that have the potential to leach from waste-disposal pits that are associated with petroleum exploration and production activities is a problem of interest to industry and regulatory agencies. A stochastic modeling approach for the migration of constituents in soil and groundwater was developed to assess the impact on groundwater at receptors that are downgradient from a waste pit. The model evaluates uncertainties in constituent concentrations in groundwater due to uncertainties in waste-composition and hydrogeologic properties of waste sites, and it determines the probability distributions of constituent concentration at receptor points by using Monte Carlo (MC), First-Order (FO), and Point-Estimate (PE) methods. Application of the FO and PE methods to assess probability distributions requires an assumption of the form of the probability density function for concentration at a receptor point. A log-normal distribution is employed here. A comparison of the three uncertainty-analysis methods is performed to evaluate the efficiency and accuracy of the FO and PE methods relative to the MC method. Results suggest that for non-reactive and conservative constituents the level of accuracy provided by FO method is similar to that of the MC method. The computational effort for the FO method is about 1 percent of that for the MC method. For nonconservative constituents, the FO method compared less favorably with the MC results. Thus, the use of the MC method is warranted, for nonconservative constituents or for cases where a higher degree of precision in the probability distribution is needed. © 1995 Springer-Verlag Berlin Heidelberg.