Abstract: A three-dimensional transient mathematical model of weld pool for a stationary tungsten inert gas welding was established based on the fluid dynamic equations. In this model, enthalpy-porosity method was used to handle liquid-solid phase change, VOF method was employed to track the free surface deformation of the weld pool. By solving these equations, the deformation behavior of surface and the distributions of temperature and velocity were obtained under the independent action by buoyancy, Marangoni force, electromagnetic force and arc pressure, respectively. The results indicate that,at high welding current (I≥250 A), a surface projection forms in weld pool when buoyancy, Marangoni force with positive temperature coefficient of surface tension and electromagnetic force were acted independently, while a surface depression formsunder the action of arc pressure, Marangoni force with negative temperature coefficient of surface tension. At high welding current, weld pool depression phenomenon appears for both TIG welding and activated flux TIG welding. For TIG welding, there exists an inward vortex in the central zone of the weld pool, while a outward vortex appears in the periphery.For activated flux TIG welding, two inward vortexes are induced by different factors in the central zone and periphery of the weld pool,respectively. The magnitude of surface deformation was not superimposed simply by each driving force.