Thermo-mechanical simulations of the Friction Stir Spot Welding (FSSW) processes were performed for AA5083-H18 and AA6022-T4, utilizing commercial Finite Element Method (FEM) and Finite Volume Method (FVM) codes, which are based on Lagrangian and Eulerian formulations, respectively. The Lagrangian explicit dynamic FEM code, PAM-CRASH, and the Eulerian Computational Fluid Dynamics (CFD) FVM code, STAR-CD, were utilized to understand the effect of pin geometry on weld strength and material flow under the unsteady state condition. Using FVM code, material flow patterns near the tool boundary were analyzed to explain weld strength difference between welds by a cylindrical pin and welds by a triangular pin, whereas the frictional energy concept using the FEM code had a limited capacity to explain the weld strength difference.