Abstract: The three-dimensional quasi-steady state mathematical model of arc in sheet slanting electrode tungsten insert gas welding is presented based on the fluid dynamic equations and Maxwell equations. The distributions of temperature field, velocity field, electrical field and current density about arc in sheet slanting tungsten electrode are obtained. The results show that the temperature field, velocity field, electric field and current density of arc are symmetric in the thickness direction of sheet slanting tungsten electrode. The maximum temperature, velocity and current density of arc in sheet slanting tungsten electrode are lower than those of arc in cylinder tungsten electrode under the similar parameters. The sheet slanting tungsten electrode can change the gap width of arc discharge to lead the current density concentrate on the location with smaller gap width, whereas the current density would also flow backward along the hypotenuse of sheet slanting tungsten electrode due to that the arc lags behind sheet slanting tungsten electrode's motion, consequently the distribution range of current density and temperature field expand in width direction of sheet slanting tungsten electrode. The local extensive distribution of current density would occur with variation of tilt angle of hypotenuse of sheet slanting tungsten electrode, and this causes the shift of cathode jet and region with higher temperature near cathode.