Use of a plasma arc as the source of energy for penetration welding of thin plates gives rise to a cylindrical hole surrounded by the molten metal. Material moves from the front to the rear of the hole by flowing around the hole as the workpiece is translated relatively to the arc. Based on the finite difference method, three different computer models have been proposed for the steady state, two dimensional heat and mass flow during the plasma arc welding. In the formulation energy equation was derived by the energy blance method through the cell control volume, and all the governing equations derived for the fixed coordinates was translated for the moving coordinate system. The driving force for fluid flow being considered was only electromagnetic force. The calculated and measured molten poon and HAZ width were compared and better agreement was obtained for the models considering the keyhole effect.