This study is devoted to the modeling of the arc formation in a direct current plasma gun newly commercialized by Saint-Gobain Coating Solutions (Avignon, France). The CFD computations were performed using the FLUENT code. The electromagnetic coupling was implemented on the basis of a three-dimensional model using additional scalars for the electromagnetic equations and user-defined functions to set up the problem. Whereas most of earlier models include the arc region only, the CFD domain was extended to the gas injection region (i.e., upstream part of the gun, including the gas diffuser), thus allowing a better description of the swirl injection on the plasma flow. Similarly, whereas numerous earlier works include the fluid domain only, the present model takes the fluid/solid coupling problem in the anode into account. In particular, the thermal and the electromagnetic equations are solved not only in the fluid parts but also in the tungsten and copper parts of the anode. This change was found to be important because the internal surface of the anode is no more a boundary of the domain. Thus, its temperature (and electric potential) becomes variable and is thus not necessarily imposed. Finally, the implemented model provides interesting results describing the arc behavior inside the plasma gun.