Abstract: Differential equation for movements of pipeline under joint actions of flowing fluid and distributed follower forces have been constructed on bases of Pflüger pillar model and common fluid-transmission pipeline models. Furthermore, divergence has been performed by using the Galerkin Method. Characteristic frequency values of modal functions can be determined through joint application of transmission matrix method and boundary conditions to determine the stability of fluid-transmission pipelines under distributed follower forces. In addition, impacts of cracking depth and position on the critical flow velocity and patterns of stability loss in fluid-transmission pipeline branch under distributed follower forces can be clarified. Research results show that deeper crack in fluid-transmission pipeline branch and longer distance between such crack and pipeline tip may generate more significant impact of distributed follower forces on stability. In addition, patters of stability loss may vary accordingly.