This paper proposes an analytic method based on finite-element method (FEM) for the rolling gaits of tensegrity robots. By analyzing forces during the rolling motions, the following problems can be solved. First, the relation between the actuator combinations (AC) and the rolling directions is discovered for controlling the rolling motions. Second, the influence of the driving parameters on the deformations is found out for obtaining the optimized control strategy. Third, the influence of the material parameters on the rolling motions is achieved as guidance to design physical robots. Tensegrity robots were proposed as novel mobile robots based on tensegrity structures that consist of discrete rigid struts and continuous elastic cables. The tensegrity structures process the shock resistance ability and high deformation capacity, and can be used to build lightweight mobile robots. The tensegrity robots can generate multiple gaits and multiple deformations. Rolling gaits are more stable than jumping and more efficient than crawling. Aiming at rolling gaits, to solve the three problems mentioned earlier, force analysis is required. The internal forces of the tensegrity structures always keep balance to maintain the shape of the structures, however, as the structures are highly coupled, the variation of one force will change the rest of the forces and generates feedback effects to this force. As the number of the forces increase with the growing number of struts, the force analysis becomes more and more complicated. The existing exhaustive experimental method can obtain the relation between the AC and the rolling directions through massive experiments, but this method cannot tell the influence of the driving parameters on the deformations and the experiment results based on certain robots are not suitable for other robots without analyzing the influence of the material parameters. In this paper, an analytic method based on FEM is introduced. A six-strut tensegrity model is used as an example to test the feasibility of the method. Experiments on a physical robot are performed to verify the reliability of the computation results.