Abstract: The fluid-structure interaction phenomenon for elastic structures with large deformation is widely observed in nature and engineering. The numerical simulation of such system involves solving flow around moving deformable boundaries. The Immersed Boundary-Lattice Boltzmann Flux Solver (IB-LBFS) is a recently developed numerical method in finite volume framework, which is also suitable for simulating flows around complex geometry in Cartesian grid. In the LBFS, the lattice Boltzmann equations at local interface are reconstructed by fluxes at cell interface. The LBFS improves the computational flexibility and efficiency substantially when compared with standard lattice Boltzmann method. The no-slip boundary condition is satisfied by using an implicit boundary condition-enforced immersed boundary method. Acceleration techniques of the IB-LBFS are presented, and a parallel code and algorithm for the IB-LBFS are developed. A fluid-structure interaction numerical platform is established joint with the Absolute Nodal Coordinate Formula (ANCF) structure solver to simulate elastic structure FSI problem with large deformation. Flows around a swilling sphere are performed to test the acceleration techniques and parallel code. Test cases for flow across a swinging flag and a clamped plate are presented for validation and are used for the comparison with traditional FSI solver.