We present, in this paper, the magnetohydrodynamic (MHD) modeling of a three-phase plasma torch. The MHD equations are solved using CFD software Code Saturne (A (R)), a computational fluid dynamics software which is based on colocated finite volume. The model developed is 3-D, time dependent, and assumes Local Thermodynamic Equilibrium (LTE). Regarding numerical issues, the modeling of the three-phase AC discharge is particularly tricky since the arcs ignition, by the rotating electrical potential, is relative to the electron density of the electrode gap middle. However, despite these challenging difficulties, the numerical model has been successfully implemented by a LTE assumption. After a detailed description of the model, the results are presented, analyzed, and discussed. The influence of current and nitrogen flow rate over the arc characteristics are studied in terms of temperature, arc behavior (position and motion), velocity and electrical potential. The model gave significant information on parameters that could hardly be obtained experimentally. This study has shown the strong influence of the electrode jets on the overall arc and flow behavior. This work is likely to open the way toward a better understanding of three-phase discharges, which technologies are currently encountering an important development in many application fields.