Abstract: Based on the large deformation theory for the extensible elastic beams, the governing equations of post-buckling of a simply supported elastic beam subjected to a distributed tangential follower force along the central axis are established. They consist of a boundary value problem of ordinary differential equations with strong non-linearity, in which seven unknown functions are included and the arc length of the deformed axis is considered as the one of the basic unknown functions. By using shooting method and analytical continuation, the nonlinear boundary-value problem is numerically solved and the equilibrium paths as well as the post-buckling configurations of the deformed beam are obtained. The results show that the features of the equilibrium paths of the beam subjected to a non-conservative load are evidently different from those to a conservative one.