Cables are lightweight structural elements used in a variety of engineering applications. In this paper an active boundary control system is introduced that damps undesirable vibrations in a cable. Using Hamilton's principle, the governing non-linear partial differential equations for an elastic cable are derived, including the natural boundary conditions associated with boundary force control. Based on Lyapunov theory, passive and active vibration controllers are developed. A Galerkin approach generates the linearized, closed loop, modal dynamics equations for out-of-plane vibration. Simulations and experiments demonstrate the improved damping provided by the active boundary controller.