The use of physical and hydraulic containment systems for the isolation of contaminated ground water and aquifer materials associated with hazardous waste sites has increased during the last decade. The existing methodologies for monitoring and evaluating leakage from hazardous waste containment systems rely primarily on limited hydraulic head data. The number of hydraulic head monitoring points available at most sites employing physical containment systems may be insufficient to identify significant leaks from the systems. A probabilistic approach for evaluating the performance of containment systems, based on estimations of apparent leakage rates, is used to introduce a methodology for determining the minimum number of monitoring points necessary to identify the hydraulic signature of leakage from a containment system. The probabilistic method is based on the principles of geometric probability. The method is demonstrated using three-dimensional ground water flow modeling results of leakage through a vertical barrier. The results indicate that the monitoring point spacing used at many hazardous waste sites likely is inadequate to detect the hydraulic signatures of all but the largest leaks.