Three-dimensional, transient simulations of the plasma flow inside different plasma spray torches have been performed using a local thermodynamic equilibrium model solved by a multiscale finite element method. The model describes the dynamics of the arc without any further assumption on the reattachment process except for the use of an artificially high electrical conductivity near the electrodes. Simulations of an F4-MB torch from Sulzer-Metco and two configurations of the SG-100 torch from Praxair are presented. The simulations show that, when straight or swirl injection is used, the arc is dragged by the flow and then jumps to form a new attachment, preferably at the opposite side of the original attachment, as has been observed experimentally. Although the predicted reattachment frequencies are at present higher than the experimental ones, the model is suitable as a design tool.