We investigate the use of cable tension for active vibration control in frame structures. A general formulation for this class of systems is developed using finite elements, which includes the dynamics of the structure and the effects of cable-structure interactions. It is found that the cable tension has two distinct effects on the structure. The first is a parametric effect in which the cable tension changes the stiffness of the structure, and the second is a direct effect that provides an external force on the structure. Based on this model, a general control scheme is developed that uses cable actuation to take advantage of these effects, both separately and together. The control scheme for all cases is based on modal amplitudes, and it applies and releases tension in such a manner that vibration energy is removed from the modes of the structure over a prescribed frequency range that depends on the bandwidth(s) of the actuator(s). The stability of the controlled systems is proven using nonlinear control theory. In addition, a method is developed for determining the optimal placement of cables for parametric stiffness control, which is verified via simulations. Finally, an experimental realization of the direct force control is tested on a frame structure and compared with simulations, demonstrating its effectiveness.