Abstract: The Computational Fluid Dynamics ofhigh-speed flight is developing in parallel with thecomputer technology. In treating the problem macroscopically, the ordinaryway of solving the Euler equations and N-S equations is improved to accountfor the real gas effect, which means including chemical reactions andionization of the gas particles. Microscopically, treating the problem byMonte-Carlo method to simulate the motion of gas particles(DSMC) isalso developed. Although theoretically the DSMC method is applicable to allkinds of flow, the computer time required for computation is enormous,therefore it is only used in special cases and themacroscopic method is mostly used. This paper discusses the hypersonic flightproblems related to the aerodynamic heating, including the choice ofthe mathematical model, the determination of chemical species and theirreactions, the treatment of boundary conditions, the calculation of theheat generated byradiation and so forth. Finally, the proper way of mathematical simulationof hypersonic flight is proposed.