Abstract: The coupling dynamic equation is established for a flexible cantilever with an axial flow channel under an impact load. Base on the dynamic Hopf bifurcation theory, the Jacobi matrix characteristic polynomial of the perturbation equation is analyzed, and the critical velocity of flutter destabilization is obtained theoretically for the liquid-solid coupling system. Then the flutter destabilization is demonstrated through numerical calculations. The damped vibration response of the flexible cantilever under an impact load is investigated within the critical flow velocity. The numerical calculations show that varying the flow velocity V has a remarkable influence on the amplitude, duration and frequency of the damped vibration, and moreover, increasing the flow velocity V within 0<V<3 is very helpful to suppress the damped vibration.