Numerical simulation results are presented in this paper concerning the heat transfer and fluid flow within the supersonic plasma jet, which is produced by the converging diverging plasma torch. The full NaiverStokes equations, which take into account the gas viscous effects, temperature and pressure dependent properties, and compressible effects, are employed in this simulation and the PHOENICS software is used to solve the set of nonlinear equations. The shock structure within the supersonic plasma jet is analysed in detail,and the effects of ambient pressure on the jet flow field are studied. Results show that the supersonic plasma flow interacts with the ambient gas and forms a series of compression and expansion waves in the region near the torch nozzle exit.