Tensegrity is a kind of spatial structural system composed of cable (in tension) and strut (in compression). Stability is provided by the self-stress state between tensioned and compressed elements. When this structure is subjected to external dynamic loading, it may become unstable due to low structural damping. In this study, the proportional damping is considered and dynamical equations of the tensegrity structure are derived based on the equilibrium configuration. In addition the mass of cable element is taken into account. In general, linearized dynamic model provides a good approximation for analyzing the nonlinear behavior of tensegrity structures around an equilibrium configuration. So, state space method is implemented to obtain the dynamic response of the tensegrity system. Two different tensegrity structures are numerically evaluated using this approach in order to show its efficiency. Results reveal how the dynamic analysis of a tensegrity structure is essential. When resonance occurs, the compressive and in-tension members of a tensegrity system may dynamically buckle and slack respectively. In addition, the results show that the computational time to evaluate a tensegrity structure using the state space method is shorter than that of Newmark algorithm.