This article presents a three-dimensional (3D) mathematical model for the plasma arc in gas tungsten arc welding (GTAW). The velocity, pressure, temperature, electric potential, current density, and magnetic field of the plasma arc are calculated by solving the mass, momentum, and energy conservation equations coupled with electromagnetic equations. The predicted results were compared with the published experimental data and good agreements were achieved. This 3D model can be used to study a nonaxisymmetric arc that may be caused by the presence of nonaxisymmetric weld pools, joint configurations, and perturbations such as an external magnetic field. This study also provides a method to calculate 3D arc pressure, heat flux, and current density on the surface of the weld pool which, if coupled with a weld pool model, will become a complete model of GTAW.