The objectives of this study were to analyze the bonding criteria for friction stir spot welding (FSSW) using a finite element analysis (FEA) and to determine the optimal process parameters using artificial neural networks. Pressure-time and pressure-time-flow criteria are the bonding criteria used to confirm the degree of bonding in solid-state bonding processes such as porthole die extrusion and roll bonding. The FEA of the FSSW process was performed with ABAQUS-3D Explicit, with the results applied to the bonding criteria. Additionally, the coupled Eulerian–Lagrangian method used for large deformations was applied to deal with severe mesh distortions. Of the two criteria, the pressure-time-flow criterion was found to be more suitable for the FSSW process. Using artificial neural networks with the bonding criteria results, process parameters were optimized for weld zone hardness and bonding strength. Among the three process parameters used, tool rotational speed was found to have the largest effect on bonding strength and hardness. Experimental results were obtained using the process parameters, and these results were compared to the predicted results and verified. The experimental value for bonding strength was 4.0 kN and the predicted value of 4.147 kN, resulting in an error of 3.675%. For hardness, the experimental value was 62 Hv, the predicted value was 60.018 Hv, and the error was 3.197%.