In order to investigate the dynamics and vortex shedding of flexible supersonic canopies, a compressible permeability model combined with fabric structure parameters is proposed, and the periodic oscillation of the supersonic parachute which is referred to as breathing phenomenon is simulated based on the Arbitrary Langrangian Eulerian (ALE) method. The calculated results by new permeability model are consistent with the experimental results. The underlying mechanism of canopy breathing motion is then investigated. Moreover, the influence of canopy permeability on breathing phenomenon of supersonic parachute is analyzed. The results indicate that the periodic growth and shedding of the canopy vortex causes the variation of the pressure differential, which finally lead to the periodic oscillation of the canopy. With the increase of fabric permeability, the vortex rolled up from the canopy skirt move backward and become more slender. The influence of vortex shedding on canopy breathing motion weakened. Those lead to the decrease of the average value of canopy projected area and parachute dynamic load. So are the oscillation amplitude and frequency. The parachute deceleration performance decreases while the parachute swing angle decreases as the canopy permeability increases.