A mathematical model of mutually coupled welding arc and weld pool is established for moving tungsten inert gas welding process on SUS304 stainless steels to investigate the argon and the helium arc properties and their effects on the weld shapes. The comparisons of the temperature contour, the current density and the heat flux on the anode surface between the argon and the helium arcs show that the helium arc is more constricted than the argon arc and transfers more heat fluxes to the anode. The effects of buoyancy, electromagnetic force, Marangoni force and drag individually on the weld pool are simulated, and simulation results show that the Marangoni force on the pool surface is one of the main forces affecting the weld shape, independent of shielding gases. Under argon arc, an other dominant force is the plasma drag force. However, the effect of electromagnetic force is stronger than that of the plasma drag force in helium arc. The inward convection induced by the electromagnetic force increases the weld depth, thereby leading the weld depth and the D/W ratio in helium arc to be larger than the ones in argon arc under the same oxygen content. The weld D/W ratio increases first and then maintains a constant with the increase of oxygen content for both argon arc and helium arc. The weld D/W ratio obtained by simulation is in good agreement with experimental results.