We examine the effect of uncertainty due to limited information on the remediation design of a contaminated aquifer using the pump and treat method. The hydraulic conductivity and contaminant concentration distributions for a fictitious contaminated aquifer are generated assuming a limited number of sampling locations. Stochastic optimization with multiple realizations is used to account for aquifer uncertainty. The optimization process involves a genetic algorithm (GA). As the number of realizations increases, a greater extraction rate and more wells are needed. There was a total cost increase, but the optimal remediation designs became more reliable. Stochastic optimization analysis also determines the locations for extraction wells, the variation in extraction rates as a function of the change of well locations, and the reliability of the optimal designs. The number of realizations (stack number) that caused the design factors to converge could be determined. Effective stochastic optimization may be achieved by reducing computational resources. An increase in the variability of the conductivity distribution requires more extraction wells. Information about potential extraction wells can be used to prevent failure of the remediation task.