A genetic algorithm combined with a static Kalman filter and a stochastic groundwater flow and contaminant transport model can be used to determine when and where to take samples to reduce the uncertainty associated with the statistical distribution describing a groundwater contamination concentration field at least cost. The use of a Kalman filter requires an initial estimate of the concentration field as well as its error covariance matrix, which are generated as the output of the simulation model. The random field input to the simulator, namely, realizations of the hydraulic conductivity field, can be generated using a Latin hypercube sampling technique. Employing the proposed optimal design strategy, a cost-effective groundwater sampling network design is realized. The proposed methodology is applied to a field problem.