This paper investigated the natural frequency and static critical flow velocity of simply supported pipes conveying fluid with both ends restrained elastically.The expression of vertical vibration modefunction of pipeline was derived from the boundary condition of simply supports with elastic restrained beam.The effects of restraining elastic coefficient,fluid pressure,fluid flow rate and axial force of pipe section on the characteristics of natural frequency and static critical instability flow velocity were calculated and analyzed based on the eigenequation.The numerical results show that the natural frequency and critical instability flow velocity are proportional to elastic restraining coefficient,but is proportional conversely to flow velocity,fluid pressure and axial sectional drawn force of pipe.It is a convenient and effective way to increase the natural frequency and critical instability flow velocity of pipeline through additional elastic restraining with proper coefficient on two ends while their values are low.