Butt welding of austenitic stainless steel 304 plates was carried out using an electron beam. Experiments were conducted for various combinations of input process parameters determined according to central composite design. Three input parameters, namely accelerating voltage, beam current, and welding speed were considered during the experiments. The weld-bead parameters, namely bead width and its depth of penetration, and weld strength in terms of yield strength and ultimate tensile strength, were measured as the responses of the process. Input–output modelling of this process was carried out in the forwards direction using regression analysis, a back-propagation neural network (BPNN), and a genetic algorithm-tuned neural network (GANN). Reverse mapping of this process was also attempted using the BPNN and GANN-based approaches, although the same could not be done from the obtained regression equations. The GANN was found to outperform the other two approaches in forward mapping. In reverse mapping also, GANN was seen to perform better than BPNN. The reason for this could have been that the back-propagation algorithm of the BPNN was replaced by a genetic algorithm in the GANN.