A key aspect of the operation of conventional non-transferred Direct Current (DC) plasma torches is the random motion of the arc inside the nozzle. Various plasma gun designs have been developed to limit the arc fluctuations without increasing the heat load to the anode wall that results in surface erosion and anode wear. However, construction of these plasma torches is highly complex while the conventional DC plasma torch consists of small number of elements and is simple to manufacture and maintain. A better understanding of the behavior of the arc-anode attachment and the way it depends on the operating conditions may help to design and operate conventional plasma torches so that the fluctuation of the time-voltage and therefore the time-enthalpy variation, is as low as possible with a fluctuation frequency adapted to the time characteristic of the powder particles in the plasma jet. This study deals with a three-dimensional (3-D) time-dependent modeling of the arc and plasma generation in such a torch operating under the so-called “restrike” mode. The latter is characterized by rather large voltage fluctuations, corresponding to a broad range of conditions used in the manufacturing of plasma coatings. The mathematical model is based on the simultaneous solution of the conservation equations of mass, momentum, energy, electric current and electromagnetism equations. It makes it possible to predict the effect of the operating parameters of the plasma torch on the motion of the anode root attachment over the anode surface, and the time-evolution of arc voltage and flow fields in the nozzle.