In present paper, a two-dimensional transient laminar model has been developed to predict the extinguishing boundary of radio frequency thermal plasma torch. The influence of the discharge frequency, gas flow rates of central, intermediate and sheath gases (Q 1 , Q 2 , Q 3 ) on the extinguishing boundary has been determined. It is found that the value of the minimum sustaining power of rf thermal plasma monotonically rises up with increasing the flow rates of carrier Q 1 and intermediate Q 2 gases. And when the flow rate of sheath gas Q 3 and the discharge frequency f increase, the value of the minimum sustaining power monotonically decreases. The results in present work could provide useful information for organizing the working gas supply system to obtain a stable discharge in induction thermal plasma torches.