A mathematical model has been developed on the continuous synthesis of fullerenes by direct evaporation of carbon-containing materials using induction thermal plasma technology. The main purpose of this study is to numerically investigate the effect of plasma gas composition and operating pressure on the fullerene formation. The simulation results confirmed that Ar-He mixture plasma is more efficient than argon plasma in terms of the particle evaporation, generation of fullerene precursors, fullerene growth and their annealing, and that low pressure operation would decrease the overall yield rate of fullerenes by enhancing the radial diffusion of carbon vapors towards the reactor walls. Thus an operating condition of relatively high helium content in the plasma gas and elevated gas pressure seems much more desirable for achieving a high yield rate of fullerenes. This conclusion is in line with the experimental evidences reported previously.