This work deals with a 3-D time-dependent modeling of the arc behavior in a plasma spray torch. The mathematical model is based on the simultaneous solutions of the conservation equations of mass, momentum, energy, electric current and the electromagnetism equations. It makes it possible to predict the motion of the anode attachment root on the anode surface under the combined effect of hydrodynamic and magnetic force and, the time-evolution of arc voltage and gas fields in the nozzle. The calculations show that the latter exhibit significant three-dimensional characteristics. The projected arc behavior and voltage fluctuations agree rather well with experimental observations.