A model of plasma-forming gas flows in AC plasma torches was proposed for the range of operating parameters typical for technologies for the synthesis of perspective materials. It assumes the solution of the Navier-Stokes equations together with the equation for the electric field potential and includes a model of arc root motion. The law of the motion was restored by the method of generative model design from the available experimental data. The COMSOL MultiphysicsR package was used for simulations. An additional analysis of the applicability of various package modules for modeling essentially subsonic compressible flows with energy release was carried out. Recommendations were given for the simulation of flows in AC plasma torches. The influence of the arc root motion on the flow pattern was studied and the significant asymmetry in the gas-dynamic parameter distributions was shown.