The hydrologic and operational characteristics associated with large surface and ground water systems are generally complex in nature. Decisions related to the best strategy of man agement of such systems have to be made using computer models which are designed to simulate both the physics of water flow a swell as the rules of operation associated with the allocation and distribution of water. A physically based hydrologic model combined with a management model could be used to simulate the physical and the operational behavior of the system. To qualify as a decision making tool for management the models should be computationally efficient to be used a large number of times with acceptable accuracies at reasonable costs. A computationally efficient numerical ground water modeling technique based on the linearsystems theory is presented. The classical Green's function method used for the solution of partial differential equations is extended for cases of finite ground water aquifers with nonhomogeneous physical properties.The computational efficiencies of the technique with respect to the computation time and storage requirements make the models ideally suited for micro and mini computers . The results of a case study conducted using the developed techniques is presented.