The numerical simulation of the parachute deployment/inflation process involves fluid structure interaction problems, the inherent complexities in the fluid structure interaction have been posing several computational challenges. In this paper a high fidelity Eulerian computational approach is proposed for the simulation of parachute deployment/inflation. Unlike the arbitrary Eulerian Lagrangian (ALE) method widely employed in this area, the Eulerian computational approach is established on three computational techniques: computational fluid dynamics, computational structure dynamics and computational moving boundary. A set of stationary, non-deforming Cartesian grids is adopted in our computational fluid dynamics, our computational structure dynamics is enhanced by non-linear finite element method and membrane wrinkling algorithm, instead of conventional computational mesh dynamics, an immersed boundary method is employed to avoid insurmountable poor grid quality brought in by moving mesh approaches. To validate the proposed numerical approach the deployment/inflation of C-9 parachute is simulated using our approach and the results show similar characteristics compared with experimental results and previous literature. The computed results have demonstrated the proposed method to be a useful tool for analyzing dynamic parachute deployment and subsequent inflation.