The vortex induced vibration(VIV) of a flexible plate behind the square head with various flow velocities is simulated. The closely coupling approach is used to model this fluid-structure interaction problem.The fluid governed by the incompressible Navier-Stokes equations is solved in arbitrary Lagrangian-Eulerian(ALE)frame by the finite volume method. The structure described by the equations of the elastodynamics in Lagrangian representation is discretized by the finite element approach. The numerical results show that the resonance occurs when the frequency of vortex shedding from square head coincides with the natural frequency of plate. And the amplitude of both the structure motion and the fluid load keeps increasing with the time. Furthermore, it is also found that in particular range of flow velocity the vibration of the plate would reach a periodical state. The amplitude of plate oscillating increases with the growth of velocity, while the frequency is locked. The vortex induced vibration (VIV) of a flexible plate behind the square head with various flow velocities is simulated. The close coupling approach is used to model this fluid-structure interaction problem. The fluid governed by the incompressible Navier-Stokes equations is solved in The structure described by the equations of the elastodynamics in Lagrangian representation is discretized by the finite element approach. The numerical results show that the resonance occurs when the frequency of vortex shedding from square And the amplitude of both the structure of motion and the fluid load keeps increasing with the time. Moreover, it is also found that in particular range of flow velocity the vibration of the plate would reach a periodical state The amplitude of plate oscillating increases with the growth of velocity, while the frequency is locked.