In this study the heat transfer and fluid flow of the molten pool in stationary gas tungsten are welding using argon shielding gas were investigated. Transporting phenomena from the welding are to the base material surface, such as current density, heat flux, arc pressure, and shear stress acting on the weld pool surface, were taken from the simulation results of the corresponding welding arc. Various driving forces for the weld pool convection were considered: self-induced electromagnetic, surface tension, buoyancy, and impinging plasma arc forces. Furthermore, the effect of surface depression due to the arc pressure acting on the molten pool surface was considered. Because the fusion boundary has a curved and unknown shape during welding, a boundary-fitted coordinate system was adopted to precisely describe the boundary for the momentum equation. The numerical model was applied to AISI 304 stainless steel and compared with the experimental results.