Existing aquifer models are either computationally inefficient or inaccurate for reservoir water-influx calculations. A new fast convolution method (FCM) that does not require lengthy data manipulation is used to implement four different single-porosity finite and infinite aquifer modeis for unsteady-state water-influx calculations. Numerical examples on circular and linear aquifers, together with a step-by-step calculation, are used to demonstrate the accuracy and efficiency of the models. These numerical studies show that the FCM approach is as much as 20% more accurate than the widely used methods for both finite and infinite aquifers. The models can be implemented readily in numerical reservoir simulators, as well as in hand computations.