The basic research of supersonic landing of parachute is an urgent need for aerospace science, especially for the deep space exploration, such as the Mars exploration. The opening, inflation and steady falling process of parachute have been studied for a long time, but the mechanism of interactions of parachute with multi-physics process, when falling at supersonic speed is still not clear, particularly whether the breathing of parachute at supersonic free falling will cause the instability and dilaceration of canopy or not, which can cause the failure of the mission. Therefore in this project, these problems will be studied with numerical simulations and supersonic wind tunnel test. The technical difficulties includes the mechanics modeling of complicated cable and membrane structures, the lightweight and flexibility of canopy, the air permeability of canopy, folding and contacting of canopy; unsteady fluid-structure coupling and complex interactions of shock waves, turbulence and boundary layer with parachute in the supersonic falling, and the numerical simulation and control of supersonic free falling of the system of parachute and re-entry capsule. All of these difficulties make the study of numerical simulation and supersonic wind tunnel test of supersonic free falling of the system of parachute and re-entry capsule to be one of the most challenging problems in aerodynamics.