Thermo-mechanical simulation of the Friction Stir Spot Welding (FSSW) processes was performed for the AA5083-H18 sheets, utilizing commercial Finite Element Method (FEM) and Finite Volume Method (FVM) which are based on Lagrangian and Eulerian formulations, respectively. The Lagrangian explicit dynamic FEM code, PAM-RASH, and the Eulerian Computational Fluid Dynamics (CFD) FVM code, STAR-CD, were utilize to understand the effect of pin geometry on weld strength and material flow under the unsteady state condition Using FVM code, material flow pattern near the tool boundary was analyzed to explain the weld strength difference between the weld by cylindrical pin and the weld by triangular pin, while the frictional energy concept using the FEM code had limitation to explain the weld strength difference.