Abstract: Based on Pflüger column model and that of a fluid-conveying pipe, the dynamic differential equation for pipes under co-action of distributed follower force and flowing fluid is established, which is then discretized with Galerkin method. By analyzing its eigenvalues, a formula is derived for calculating the critical flow velocity for divergence, and the complex frequencies versus the flow velocity are obtained for different parameters. By solving the discretized equations with Runge-Kutta numerical integration, the displacement time-history and the phase diagrams of the pipes are given for different parameters. The numerical results show that: the dimensionless critical flow velocities for divergence for pipes conveying fluid with distributed follower force are irrelevant to the mass-ratio, and those for flutter increase slightly with increasing mass-ratio; the critical flow velocities for both divergence and flutter decrease notably as the distributed follower force increases; with increasing mass-ratio, the increase-rate of the displacement of pipes in divergence and the amplitude of fluid-induced vibration increase. In the absence of distributed follower force or of flowing fluid, the results are in good agreement with known ones.