Abstract: Fluid-structure interaction (FSI) for structures with large deformation is a crucial problem in aerodynamics, hydrodynamics and bio-fluid mechanics. An efficient numerical method is needed in FSI modeling and analyzing flow over elastic structures. A new FSI solver, which adopts the recent developed Cartesian flow solver called immersed boundary-lattice Boltzmann flux solver (IB-LBFS) and the structure solver of finite element absolute nodal coordinate formulation (ANCF), was developed and validated. Acceleration techniques of the IB-LBFS were applied and a parallel computation framework was implemented. The dynamic behaviors of a square parachute and a cross parachute during inflation were performed with the current IB-LBFS/ANCF FSI solver. Aerodynamic characteristics and the elastic configuration were obtained for different material Young's modulus.