A three-dimensional quasi-steady state mathematical model for the coupled arc in double electrode tungsten inert gas (TIG) welding is established based on the fluid dynamic equations and Maxwell equations under the reasonable boundary conditions. By solving these equations, the distributions of temperature, velocity, arc pressure and current density of the coupled arc are obtained. The results accord well with previous experimental results. It is found that the maximum temperature and plasma velocity of the coupled arc decrease compared with those of the TIG arc in the similar conditions. The peak value of arc pressure and current density at the anode surface decline sharply. Both the electrode spacing and arc length have significant influences on temperature and flow field, current density, and arc pressure of the coupled arc. Furthermore, coupled arc pressure and current density at the anode cannot be described by Gaussian assumption.