The influence of vibrational-dissociation kinetics on mass and heat transfer in non-equilibrium flows of N2/N and O2/O mixtures behind shock waves is investigated on the basis of the state-to-state approach. A method of the numerical solution of coupled equations of gas dynamics and state-to-state kinetics in the commercial flow solver ANSYS Fluent is proposed. Based on the proposed numerical tool, the flows near a cone and behind a planar shock wave are studied. The calculation results are compared with available experimental data.