Abstarct: The space structure appositest structure for large span. The space structure is a structural system that involves three dimensions. in practice, the term Space structure is simply used to refer to a number of families of structures that include grids, barrel vaults, domes, towers, cable nets, membrane systems, foldable assemblis and tensegrity forms. Tensegrity structures are spatial reticulated systems that contain a discontinuous set of compressive members (struts) inside a continuous set of tensile members(cables) whitch are stabilized by a selfstress state. Tensegrity structures are special types of structures in which prestress should be applied in order to stiffen the structure and the analysis is baxsed on the prestressed stats. other reasons, prerupture or slacking of tensile members, loss of strain hardening for tensile members in post pelastic region and so possibility of tension failure mechanism, and finally structural nonlinear behavior due changing statu. In this thesis, after definition of tensegrity structures and descxription of various configurations on these structures is reviewed. then in order to investigate the statically stability behavior of of tensegrity structures and representation of suitable responses about the rule of various parameters on reducing and increasing the feasibility of propagation of instability phenomena in the tensegrity structures, using finite elements modeling, the nonlinear analyses is performed on these structures. The modeling tensil element used multilinear isotropic. In this research, tonsion and compression failure mechanisms are studied. In each of these mechanisms, the effects of various parameters such as: slenderness ratio and the rate of initial imperfection of compressive elements, changes in initial strain and cross section of tension elements, on the instability behavior and the type of collapse in tensegrity structures are investigated. Finally, baxsed on the obtained results, several ways are put forward to prevent the occurrence of the overall collapse mechanisms and receiving the local collapse mechanisms and design recommendations. The overall collaps mechanism not proper. Because its not occure without womearn previous. Local collapse mechanism not sudden and buckling of compressive members proper than nodal snap through. Thouse design recommendations present for prevent of the overall collapse mechanism.