A new optimization formulation for designing groundwater plume control systems is presented. The new formulation uses particle-tracking techniques in a two-step solution process. The two-step procedure is motivated by numerical and computational considerations; particle representation is defined to take advantage of specific properties and improve model convergence. The optimization formulation seeks the least cost control system that satisfies the two equivalent requirements that the contaminant plume be located within the capture zone (step 1) and that all particles representing contaminant solute travel to an extraction well (step 2). To date, optimization formulations for plume capture design have emphasized either hydraulic or concentration control; however, these formulations provide indirect representation of the plume control and containment problem. The model presented here explicitly represents the capture zone design problem using particle tracking and formalizes the design procedures used by many practitioners. Two example problems representing two- and three-dimensional flow systems are used to demonstrate the new advective control model. Hydraulic control formulations for the two problems are also developed, and designs are compared with those of the advective control model. Control systems resulting from the hydraulic control model are sensitive to constraint magnitude and location, highlighting the need for constraint calibration in order to best achieve design goals. Conversely, constraints in the new model directly represent the plume capture problem, and the model provides more efficient capture zone designs than the hydraulic control formulation. ¿ 1999 American Geophysical Union