Achieving an effective utilization and exploitation of TIG welding arcs require a thorough understanding of the plasma properties and its physical processes. Through simultaneous solutions of the set of conservation equations for mass, momentum. Energy and current. a mathematical model has been developed to predict the velocity, temperature, and current density distributions in argon welding arcs. The predicted temperature fields in arc regions, and the distribution of current density and heat flux at the anode agree well with measurements reported in literatures. This work could lay the foundation for developing a comprehensive model of the TIG welding process wheve a dynamic, two-way coupling between the welding arc and the weld pool surface is properly represented.