A thermal and chemical non-equilibrium model is developed for the modelling of multi-component supersonic induction Ar-H2 plasma flows. The species included in the modelling are electrons(e), hydrogen ion(H+), hydrogen atoms(H), hydrogen molecules(H2), Argon ions(Ar+) and Argon atoms(Ar). The negative hydrogen ions(H-), molecular hydrogen ions(H2+) and second order ionisation are neglected. The chemical reactions considered in the modelling are the H2 dissociations and the corresponding recombination, induced by Ar atom and H2, and the ionisations of the hydrogen and Argon and the corresponding recombination. All the heavy species are assumed to have the same temperature (Ti). The electron temperature (Te) is allowed to deviate from that of heavy species. The energies for these chemical reactions have been treated as the source terms for energy conservation equations. As a result, the contributions of these chemical reactions to the total enthalpy are removed. Therefore, the heavy species temperature can be obtained by solving the thermal kinetic energy equation, rather than the total enthalpy equation. Yos’s mixing law is used to calculate the contribution of vibrational and rotational energies of hydrogen molecules to the thermal conductivity of heavy species. The transport properties are calculated using the formulas derived by Hirschfelder, Curtiss and Bird. The data of collision integrals or collision cross-sections between species in the mixture are taken from Murphy, Devoto and Mason’s publications. The binary mass diffusion coefficients between the species in the mixture are also calculated from these collision integral data. The mass diffusion of species in the mixture are modelled under the dilute approximation at present since the mole fraction of the principal species, Argon, in the whole computational region is more than 90%. For charged species, Ambipolar diffusion coefficients are used. Mass balance equations are solved to obtain the mass fractions or mole fractions or the number densities of all the species except for electrons. The electron number density is determined by the condition of electrical neutrality. The developed model is applied to the modelling of inductive plasma flow, generated by the Tekna PL-35 torch model, under different pressures and then to the supersonic plasma flow. The model has been validated by comparing the transport properties under the LTE conditions from this model with the corresponding published values.