Suitable selection of various machining parameters for wire electrical discharge machining (WEDM) process heavily relies on the operator’s experience and manufacturer’s technologies because of their numerous and diverse operating ranges. Artificial neural networks have been introduced as an effective tool to predict values of responses and input parameters of different machining processes through forward and reverse modeling approaches respectively. This paper mainly focuses on predicting values of some machining responses, like machining rate, surface roughness, dimensional deviation and wire wear ratio using feed forward back propagation artificial neural network based on six WEDM process parameters, such as pulse on time, pulse off time, peak current, spark gap voltage, wire feed and wire tension. The corresponding reverse model is also developed to recommend the optimal settings of WEDM process parameters for achieving the desired responses according to the requirements of the end users. These modeling approaches are quite efficient to predict the values of machining responses as well as process parameter settings with reduced time and effort which otherwise have to be determined experimentally based on trial and error method. The predicted results are found to be in well congruence with the previously obtained experimental observations.