A stochastic modeling approach for the migration of contaminants in soil and ground-water is developed to assess the expected magnitude of contamination at receptors located downgradient from a waste pit. The model evaluates uncertainties in contaminant concentrations due to uncertainties in waste composition and hydrogeologic properties of waste sites, and determines the exceedance probabilities of a specified concentration level at receptor points using Monte Carlo (MC), first order (FO), and point-estimate (PE) methods. A lognormal distribution is assumed for concentration at a receptor point in application of the FO and PE methods to assess exceedance probabilities. A comparison of the three error-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 nonadsorbing and conservative contaminants, the level of accuracy provided by the FO method is comparable with that of the MC method. For nonconservative contaminants, both FO and PE methods compared less favorably with the MC results.