An improved methodology for flow structure interaction problems involving large structural deformations and all speeds in a cost-effective and accurate manner is developed. A particle-based meshless method for the structural deformations (called material point method or MPM) is integrated with a Cartesian-based flow solver. The development of the MPM and the integration with the all speed flow solver that embodies the hybrid immersed boundary (HIBM) method for handling complex deforming and moving geometries on any grid (Cartesian or curvilinear) is discussed in this paper. Two features of this integrated approach make it very suitable for inflatable Entry, Descent, and Landing (EDL) systems: 1) the MPM enables simulation of large of deformations of the EDL system from its packed to fully open state since it is a meshless method, and 2) it is possible, at low computational cost, to simulate interaction of the inflating EDL with the surrounding gas flow due to the use of the HIBM that allows the solution of an arbitrary moving and deformable body. Simulations have been performed for a tension cone geometries in its fully-inflated stage. Validation tests for HIBM in supersonic flows and for the MPM have been completed.