In　this　contribution,　a　nonlinear　formulation　of　the　equilibrium　problem　of　the　von　Mises　truss　(or　two-bar　truss)　is　presented.　The　bars　are　regarded　as　three-dimensional　bodies　composed　of　a　homogeneous　and　isotropic　material.　The　displacement　fields　are　written　under　the　assumption　of　homogeneous　deformations　and,　consequently,　the　boundary-value　problem　is　formulated.　The　relations　governing　the　equilibrium　of　each　body　are　thus　derived　and　the　global　equilibrium　of　the　von　Mises　truss　under　a　general　loading　condition　is　written.　The　stability　of　the　equilibrium　solutions　is　assessed　through　the　energy　criterion.　An　application　considering　a　compressible　Mooney-Rivlin　material　shows　interesting　post-critical　behaviors,　involving　snap-through　and　multiple　branches.　©　Springer　Nature　Switzerland　AG　2020.