Abstract: In this computational study, a gliding arc plasma reactor with a reverse-vortex flow stabilization is modelled for the first time by a fluid plasma description. The plasma reactor operates with argon gas at atmospheric pressure. The gas flow is simulated using the k-ε Reynolds-averaged Navier–Stokes turbulent model. A quasi-neutral fluid plasma model is used for computing the plasma properties. The plasma arc movement in the reactor is observed, and the results for the gas flow, electrical characteristics, plasma density, electron temperature, and gas temperature are analyzed.