The synthesis of solid BN in thermal plasma is investigated theoretically by computing the equilibrium composition of a gas mixture containing boron, nitrogen, hydrogen and argon. The calculations are done for the temperature range between 500 and 6000 K and the total pressure in the system of I bar. They are based on the fact that thermal plasma is in local thermodynamic equilibrium, which makes possible theoretical determination (by employing the Gibbs free energy data for the compounds present in the system) of its equilibrium composition. From the calculated compositions of investigated gas systems, the temperature zones with saturated and/or oversaturated vapour of B and B2N are determined and the formation mechanism of BN in solid state is proposed.