Abstract: Structural damage under blast loading always involves strong nonlinear shock-wave, extreme deformation, damage and breakage of solid structures, and strong fluid-solid interaction, which bring great difficulties to numerical simulation. In this paper, a novel immersed multi-material finite volume-material point method (iMMFV-MPM) is proposed to model the structural damage under blast loading. The multi-material finite volume method (MMFVM) is used to simulate the flow of explosives and surrounding air and specifically a TVD Riemann solver is adopted for shock simulation, while the material point method (MPM) is employed as solid solver for simulation of extreme deformation problem. The continuous-forcing immersed boundary method based on Lagrangian multiplier (lg-CFIBM) is extended to multi-material fluid to impose boundary conditions at the FSI interfaces. The lg-CFIBM can guarantee the boundary velocity conditions strictly at each time step and has no need to reconstruct FSI interfaces explicitly, which can effectively simulate the interaction between the explosion products and the building structure, the evolution of the shock wave around solid structure, and the dynamic fracture and topological change of the structure. Several numerical examples, including the damage pattern of a square reinforced concrete slab under close-in explosion, the structural damage of buildings under blast loading and the multi-chamber implosion tests, are simulated to verify and validate the proposed FSI algorithm, and numerical results are in good agreement with experiments.