This paper describes a new vibration-suppression technique for flexible cantilevered structures by using a pipe containing an internal flow. The stability and dynamic response are analyzed based on the finite element method. The flutter limit and optimum stabilizing fluid velocity are determined in root locus diagrams. The impulse responses of the system are studied by the mode superposition method to observe the damping rate of the motion. The stabilizing effect of an internal flow is demonstrated by impulse responses of the structures with and without an material damping. It is found that the response of the pipe with flow of liquid has a larger effect of, stabilizing than that with flow of gas.