Simulation of sub- and supersonic thermochemical equilibrium flows in plasmatrons is considered. A physicochemical model, numerical method, and computation results for equilibrium inductive coupled plasma flows in a plasmatron are given. An effective preconditioning technique along with an implicit total-variation-diminishing scheme is used to solve the Navier-Stokes equations in both subsonic and supersonic regimes. The governing equations include source terms corresponding to the electromagnetic field influence: the Lorentz force components (so-called magnetic pressure) and Joule heat production. The necessary transport coefficients were calculated in advance for equilibrium air plasma as the functions of pressure and temperature. Transport properties were calculated by the precise formulas of the Chapman-Enskog method in the temperature range 300 ≤ T ≤ 15,000 K. Calculations of equilibrium air plasma flows for the IPG-4 (Institute for Problems in Mechanics, Russian Academy of Science) discharge channel geometry with the channel radius R c = 0.04 m and length Zc = 0.40 m were performed. Creation of both underexpanded and overexpanded jets exhausted from the plasmatron channel is considered. A comparison with experimental results is given.