Accurate estimation of water influx into a petroleum reservoir is very important in many reservoir-engineering applications, such as material balance calculations, design of pressure maintenance programs, and advanced reservoir simulation studies. These applications have relied heavily on the classical work of van Everdingen and Hurst for edge-water drive reservoirs and on the results presented by Coats and Allard and Chen for bottom-water drive reservoirs. However, for both types of reservoirs, the determination of the values of water influx is not a straightforward task. Table lookup and interpolation between time entries are needed, and furthermore, for finite aquifers, interpolation between tables may also be required. This paper presents neural network (NN) models for the prediction of dimensionless water influx and dimensionless pressure for finite and infinite edge- and bottom-water drive reservoirs. Several neural network architectures using back-propagation with momentum for error minimization were investigated to obtain the most accurate results. In order for these NN models to be applied for a wide range of systems, dimensionless groups characterizing water influx were employed. The advantage of the proposed NN models is providing accurate results in minimum time. Furthermore, they can be easily integrated within general reservoir management programs to determine the aquifer effect on oil and gas production.