In this work, a theoretical approach via artificial neural networks model has been followed for studying the water gas shift reaction in hydrogen selective membrane reactors, based on an experimental campaign useful for training the aforementioned model. In particular, such parameters as the reaction pressure (from 150 to 300 kPa), reaction temperature (from 300 to 360 °C), gas hourly space velocity (GHSV) between 2000 and 6000 h−1, sweep gas flow rate (between 35.75 and 130.42 mL/min of N2), H2O/CO feed molar ratio (from 1/1to 4.5/1) and feed configuration (co–or counter-current mode with respect to the sweep gas) have been considered from both a modeling and an experimental point of view in order to analyze their influence on the water gas shift performance (in terms of CO conversion, hydrogen recovery, hydrogen permeate purity) in two membrane reactors, allocating dense Pd–Ag membranes, having different active membrane surface areas. As best experimental results, by using a Cu–Zn based catalyst, at GHSV = 3340 h−1, T = 350 °C, H2O/CO feed molar ratio = 2/1 and co-current configuration of sweep gas, CO conversion around 100% and H2 recovery of about 70% were reached. Meanwhile, the artificial neural networks model has been validated by using part of the experimental tests as training values and, then, it was used for optimizing the system to achieve as much as possible high hydrogen recovery. The model predicted the experimental performance of the water gas shift membrane reactors with an error on CO conversion lower than 0.5% and around 10% for the H2 recovery over the experimental tests not used during the model training.