In　this　paper,　equilibrium　and　stability　of　the　von　Mises　truss　subjected　to　a　vertical　load　are　analyzed　from　theoretical,　numerical　and　experimental　points　of　view.　The　bars　of　the　truss　are　composed　of　a　rubber　material,　so　that　large　deformations　can　be　observed.　The　analytical　model　of　the　truss　is　developed　in　the　fully　nonlinear　context　of　finite　elasticity　and　the　constitutive　behavior　of　the　rubber　is　modeled　using　the　Mooney–Rivlin　law.　The　constitutive　parameters　are　identified　by　means　of　a　genetic　algorithm　that　fits　experimental　data　from　uniaxial　tests　on　rubber　specimens.　The　numerical　analysis　is　performed　through　a　finite　element　(FE)　model.　Differently　from　the　analytical　and　FE　simulations　that　can　be　found　in　the　literature,　the　models　presented　in　this　work　are　entirely　developed　in　three-dimensional　finite　elasticity.　Experiments　are　conducted　with　a　device　that　allows　the　rubber　specimens　to　undergo　large　axial　deformations.　For　the　first　time,　snap-through　is　observed　experimentally　on　rubber　materials,　showing　good　agreement　with　both　theoretical　and　numerical　results.　Further　insights　on　Eulerian　buckling　of　the　rubber　specimens　and　its　interaction　with　the　snap-through　are　given.　A　simple　formulation　to　determine　the　critical　load　of　the　truss　is　presented　and　its　accuracy　is　validated　through　experimental　observation.　Comparisons　with　a　linear　elasticity　based　approach　demonstrate　that　an　accurate　prediction　of　snap-through　and　Eulerian　buckling　requires　nonlinear　formulations,　such　as　the　ones　proposed　in　this　work.　©　2021　Elsevier　Ltd