Abstarct: The Tensegrity Systems are a specific type of Space frxame Structures (SFS) in which cables are used as the alternative tension members. A series of tensile and compressive elements are assembled in a self-equilibrated state, which provides stability and rigidity to the system. The study of Tensegrity structures is distinct from other type of the SFS due to specific features, which include: 1) the need for applying self-tensioning for creating stiffness; 2) the lack of strain hardening for tensile members after the plastic region; 3) the possibility of loosening and tightening of the tension members. In this research, the Tensegrity Structures are treated as special type of SFS. The principles and the basic concepts of these structures along with the relevant method of analysis for the structural Tensegrity (geometric and material nonlinearities) are presented. The appropriate configuration for a¬ Tensegrity pedestrian bridge has been selected for the architectural considerations. After geometric modeling and finite element configuration, the structure, under different levels of Self-tensioning and different ratio of cable stiffness to strut, was analyzed using the Abaqus software¬. The results obtained from the analysis indicated that in the fixed stiffness ratio of the cable to the strut, increasing of self-tensioning levels do not affect the initial stiffness of the structure, but the ultimate load is slightly affected. However, it is quite effective on the increasing load on the stiffening starting point, thereby, reducing the final displacement of the structure. Also in the fixed self-tensioning levels, increasing of stiffness ratio of the cable to the strut, do not affect the ultimate load of the structure, But the initial stiffness of the structure increases. However, it is quite effective on the increasing load on the stiffening starting point, thereby, reducing the final displacement of the structure. Two types of system failure were observed: overall failure and local failure without Dynamic Snap-Through. The method to prevent undesirable failure mechanisms (overall) and to guide it to desirable failure mechanisms (local) has been presented.