Nonequilibrium flows of a two-component oxygen mixture O₂/O behind a shock wave are studied with due allowance for the state-to-state vibrational and chemical kinetics. The system of gas-dynamic equations is supplemented with kinetic equations including contributions of VT (TV)-exchange and dissociation processes. A method of the numerical solution of this system with the use of the ANSYS Fluent commercial software package is proposed, which is used in a combination with the authors’ code that takes into account nonequilibrium kinetics. The computed results are compared with parameters obtained by solving the problem in the shock-fitting formulation. The vibrational temperature is compared with experimental data. The numerical tool proposed in the present paper is applied to study the flow around a cylinder.