Hydraulic containment of a groundwater plume is modeled as a pump-and-treat system of extraction wells in a confined aquifer with uncertain transmissivity. The transmissivity is modeled as a random field with a specific covariance structure, conditioned at measurement locations. The response matrix method is used to form a linear program to obtain the optimal pumping strategy. High reliability is achieved by employing a multipole realization or ''stacking'' method which requires the solution to simultaneously satisfy a number of realizations of the random field. Empirical tests indicate that this reliability is a monotonically increasing function of the number of stacked realizations and appears to be relatively insensitive to moderate changes in the variance, correlation length, and covariance structure of the stochastic transmissivity and to changes in the boundary conditions and measurement data. Two simple statistical models based on Bayesian analysis and order statistics are formulated, leading to predicted reliabilities of (N+1)/(N+2) and N(N+1), respectively, where N is the number of stacked realizations. These simple curves are shown to compare quite well with the empirical findings. These results indicate that it may be possible to determine the stack size necessary to achieve a prespecified reliability. The robustness of the reliability curve indicates that it may be useful as a preliminary design tool for aquifer management. ¿ American Geophysical Union 1993