Abstract: Immersed boundary method is one of the important numerical methods for solving the interaction between a flexible elastic structure with large deformation and viscous fluid. The fluid-induced vibration of a cantilever beam attached to a cylinder/square immersed in incompressible fluid is simulated using the hybrid finite difference/finite element immersed boundary method combined with a traditional feedback force method. The immersed boundary method uses hyper-elastic constitutive laws with a finite element discretization of the structure and an adaptive refined Cartesian grid with a finite difference discretization of the fluid. The vibrating characteristics of a flexible hyper-elastic structure and the motion of fluid are obtained. Comparisons between the results of the paper and that of other references show the reliability of this method.