Abstract <p>Stability analysis of a fluid-conveying pipe under coaction of distributed follower force and elastic supports is conducted to work out problems like fluid-conveying pipe instability induced by pipe-flow coupling vibration in the petrochemical, aerospace, deep sea and other important engineering fields. The elastic support and the differential equation of fluid-conveying pipe motion under the coaction of flowing ore-water mixture and distributed follower force are established based on the Dirac function and Bernoulli-Euler beam model. The Galerkin method is used to discretize the differential equation by taking the mode shape function of the beam as the trail function. The results show that only flutter vibration instability occurs in the system when the elasticity coefficient is smaller than a critical value, while both divergence instability and flutter vibration instability occur in the system when the elasticity coefficient is larger than the critical value. With the increase of the distributed follower force, the critical velocity of instability decreases; the critical velocity of divergence instability is independent of the mass ratio, but the critical velocity of flutter vibration instability increases with the increase of the mass ratio. The research results provide a theoretical basis for the determination of critical flow velocity and cross-sectional dimensions within the fluid-conveying pipe, as well as the treatment of constraints at both ends.</p>