Abstract: The dynamic stability of pipes conveying fluidwith both ends supported elastically is investigated. Thevertical vibration modal function of pipeline supported elastically on twoends is derived from the boundary condition of the elastic supported beam. Theeffect of supporting elastic coefficient, mass ratio, fluid pressure andaxial force on critical instability flowrate is calculatedand analyzed based on the eigenequation. The numerical results show that thestability of pipe is complicated because the dynamic stability varieswith different elastic supporting coefficients and parameters acting on thepipe. Dynamic flutter instability will occur with a certain low elasticcoefficient and in some parameter ranges and the static instability will happenunder a high elastic coefficient and high parameters acting on the pipe. Thecritical instability flowrate is proportional conversely to fluid pressureand axial compression force of pipe section, but is proportional to theaxial tensile force.