A three-dimensional groundwater management model is developed for a shallow, unconfirmed sandy aquifer at a Superfund site at which a vinyl chloride plume is migrating toward Lake Michigan. We use nonlinear simulation-regression applied to a transient groundwater flow model to estimate parameter values and their uncertainties and use steady state flow path analyses to confirm the model's consistency with the location of contaminants. Parameter uncertainty is translated into flow model prediction uncertainty using a first-order Taylor series approximation. Optimal minimum-pumping strategies for steady state hydraulic containment of the plume are designed, and model prediction uncertainty is accounted for with stochastic programming. It is impossible to achieve a reliability level higher than 60% using only two pumping wells. For the 10-well case, pumping rate must increase about 40% to extend reliability from 50 to 90%. Monte Carlo analyses indicate that for the 10-well 90% reliability formulation, the first-order method of propagating uncertainty results in a solution with accurate performance reliabilities. We find that the coefficient of variation in hydraulic gradient dictates whether the probabilistic constraints are obeyed. Comparison of the probabilitistic constraint and ''safety factor'' approaches to overcoming model uncertainty reveals that the ability of probabilistic constraints to accommodate local variations in model prediction uncertainty is highly important. Postoptimization solute transport studies show that increased reliability levels for hydraulic containment do not necessarily translate into faster plume cleanup times. ¿ American Geophysical Union 1993