We use the front tracking method on a spring system to model the dynamic evolution of parachute canopy and risers. The canopy surface and the riser string chord of a parachute are represented by a triangulated surface mesh with preset equilibrium length on each side of the simplices. The stretching and wrinkling of the canopy and its supporting string chords (risers) are modeled by the spring system. The spring constants of the canopy and the risers are chosen based on the analysis of Young's surface modulus for the canopy fabric and Young's string modulus of the string chord. Damping is added to dissipate the excessive spring internal energy. The current model does not have radial reinforcement cables and has not taken into account the canopy porosity. This mechanical structure is coupled with the incompressible Navier–Stokes solver through the “Impulse Method”. We analyzed the numerical stability of the spring system and used this computational module to simulate the flow pattern around a static parachute canopy and the dynamic evolution during the parachute inflation process. The numerical solutions have been compared with the available experimental data and there are good agreements in the terminal descent velocity and breathing frequency of the parachute.