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Tensegrity systems composed of tension elements and compression elements have potential to be used as configurable structures and locomotive robots. A general mathematical model for controllable tensegrities is proposed. A method combining genetic algorithm (GA) and dynamic relaxation method (DRM) is developed to solve the model. Two typical applications of the proposed model and method on the shape control problem and the locomotive control problem of tensegrity systems are given. In the first application, the shape control of a two-stage tri-prism tensegrity is considered and a collision-free path with minimum energy consumption is found by the approach. In the second application, the gait design and path planning of a six-strut tensegrity is considered and optimal gaits and motion paths are obtained by the approach. The generality and feasibility of the proposed approach is conceptually verified by the applications.