We present a fluid-structure interaction methodology for compressible flow over deformable parachutes using large-eddy simulation with adaptive structured mesh refinement. The deformation of the fabric of the parachute is described by thin-shell finite-element method. Boundary conditions on the flow owing to the structures are incorporated thanks to an immersed geometry method appropriate for infinitely thin structures. The method is responsible for generating equivalent forces directly into the Navier-Stokes equations using a feedback scheme. The communication between the fluid (Eulerian) and the structural (Lagrangian) meshes is achieved by an interpolation procedure using Peskin’s numerical delta distributions. Simulations results of the new methodology are presented in this paper.