Friction welding is a promising technique for the welding of dissimilar metals. This study deals with the welding of two different alloys, namely, AISI 304 and AISI 1040. The welding process parameters, namely, friction pressure, friction time, forging pressure, and forging time were optimized for maximum tensile strength using a response surface methodology (RSM)-based technique and an adaptive-network-based fuzzy inference system (ANFIS) model. The predicted responses obtained using the ANFIS model were more accurate compared to those obtained using the RSM. From among the four input parameters examined in the study, the frictional pressure was found to be the most influential. The ANFIS model developed in this study shows significant promise as a predictive technique that can provide reasonable estimates of tensile strength for different welding parameters.