Various issues of numerical simulation of high-enthalpy non-equilibrium flows of a gas mixture of CO ₂, CO, O ₂, O, and C are discussed. Navier–Stokes equations are considered within the framework of one-, two-, and three-temperature approximations with allowance for chemical reactions. In the one-temperature approximation, chemical reactions are modelled by the Arrhenius law. In the multi-temperature approximations, simulations are performed with the use of the Treanor–Marrone model for carbon dioxide dissociation and the Park model for dissociation of diatomic gas molecules, which take into account vibrational non-equilibrium of molecules. The Arrhenius law is also used for calculating recombination reactions and also forward and backward exchange reactions. Translational-vibrational and vibrational-vibrational energy exchange is simulated by a simplified Landau–Teller model. Some examples of flows with the use of the above-mentioned approximations are calculated. It is demonstrated that the one-temperature approach ensures an adequate reproduction of experimental data on the shock standoff distance, heat flux, and pressure coefficient on the cone, which are obtained in a high-enthalpy wind tunnel. The calculation of the flow around a cylinder under Martian re-entry conditions reveals a significant effect of thermochemical non-equilibrium.