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In this paper the Artificial Neural Network (ANN) model is developed to predict the surface roughness in Wire Electrical Discharge Machining (WEDM) of Cr-Mo-V alloyed special steel, which is used in automobile industry. The neural network Models strained with experimental results conducted using L16 orthogonal array by considering the input parameters such as pulse duration, open voltage, wire speed and dielectric flushing pressure at four different levels. The mathematical relation between the work piece surface roughness and WEDM cutting parameters is also established by multiple regression analysis method. Predicted values of surface roughness by Back-propagation (BPN), General regression neural networks (GRNN) using MATLAB NN tool and regression analysis, were compared with the experimental values and their closeness with the experimental values. The predicted values in BPN network with two hidden layers are very close to the experimental results than GRNN network and multiful regression values.