A mathematical model is developed for predicting the steady-state flow pattern for a water distribution system consisting of conduits, pumps, pressure-reducing valves, and reservoirs. The model is a computerized numerical simulation of the network. Because each component of the network is governed by a nonlinear flow formula, the equilibrium of flow in the network is governed by a system of nonlinear equations. The solution to this system is sought by the Newton iteration method. The model is verified against the Hardy Cross method and applied to the determination of the flow pattern of an actual water network.