Large span reticulated structures are applied in a variety of engineering applications. Many of these structures present a nonlinear behavior involving both geometric and material nonlinearities with multistable configurations. Particularly, bistable structures are often subjected to instability phenomena, such as snap-through and bifurcations of the whole structure, individual units or single bars. The present work, focuses on two classes of bistable structural systems: pyramidal trusses (undesired instability) and deployable scissor structures (desired design instability). Theoretical and computational tools are developed to investigate the influence of the strain measure, elasto-plastic deformations and instability phenomena on the nonlinear static and dynamic response of bistable pyramidal trusses. A compliant corrotational spatial joint finite element formulation with finite size is developed and applied to study bistable deployable scissor modules. The analysis of bistable large span structures formed by the assembly of modules is also carried out. It s shown that the presence and interaction of the studied buckling sources have deep influence on the systems behavior and can ultimately determine their viability in practical applications.