Management of groundwater contamination is a very cost-intensive proposition filled with conflicting objectives and substantial uncertainty. A critical source of this uncertainty in groundwater problems comes from the data for the conductivity values for the aquifer on which the flow and transport of the contaminant is dependent. For a remediation solution to be reliable in practice it is important that it is robust over the error in modeling data. This paper presents our efforts to model the uncertainty for the Umatilla Chemical Depot site at Oregon, a difficult task given that the scarcity of available data precludes use of stochastic hydraulic conductivity generation techniques. The installation's modeling team has divided the site into conductivity zones. We use the results from various pumping tests to establish plausible ranges for the hydraulic conductivity value in each zone. Realizations for each zone are then generated randomly from these ranges. The hydraulic head conditions resulting from each realization are then compared with measured head conditions. To incorporate spatial as well as quantitative differences in the comparison, the first moments of the hydraulic head scenarios are also compared. Unrealistic realizations are eliminated and the remaining realizations are ranked based on the moment values. The ranked realizations will be used for efficient sampling using Latin Hypercube Sampling within the framework of an advanced stochastic multi-objective genetic algorithm to obtain robust, reliable and optimal solutions.