Abstract: The dynamic behavior and the stability of simply supported elastic rods with internal elastic supports under the action of uniformly distributed tangential follower force are investigated. For rods with internal elastic supports, the governing differential equations at each section and continuous conditions at internal elastic supports as well as boundary conditions are given. Simply supported elastic rods with internal elastic supports are studied using the finite difference method. Recurrence formulas for governing differential equations and discrete formulas for continuous conditions at internal elastic supports as well as boundary conditions are derived respectively. Graphical results are presented to show the effects of elastic constants of the internal elastic supports, locations of the elastic supports and moment of inertia on vibration frequencies and stability of simply supported rods. The present method is applicable to complex eigenvalue problems of non-conservative rods with internal elastic supports and complicated boundary conditions.