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Tensegrity systems composed of tension and compression elements have the potential for use in configurable structures and locomotive robots. In this work, we propose a general mathematical model for controllable tensegrity structures. Additionally, a method combining a genetic algorithm (GA) and dynamic relaxation method (DRM) is developed to solve the model. Our proposed model and method are applied to a typical shape controlled tensegrity and a typical locomotive tensegrity system. Firstly, the shape control of a two-stage tri-prism tensegrity is considered, and a collision-free path with minimum energy consumption is identified by using our approach. Secondly, gait design and path planning of a six-strut tensegrity is considered, and optimal gaits and motion paths are obtained by using our approach. The generality and feasibility of the proposed approach is conceptually verified in these implementations.