This　paper　deals　with　the　equilibrium　problem　of　von　Mises　trusses　in　nonlinear　elasticity.　A　general　loading　condition　is　considered　and　the　rods　are　regarded　as　hyperelastic　bodies　composed　of　a　homogeneous　isotropic　material.　Under　the　hypothesis　of　homogeneous　deformations,　the　finite　displacement　fields　and　deformation　gradients　are　derived.　Consequently,　the　Piola-Kirchhoff　and　Cauchy　stress　tensors　are　computed　by　formulating　the　boundary-value　problem.　The　equilibrium　in　the　deformed　configuration　is　then　written　and　the　stability　of　the　equilibrium　paths　is　assessed　through　the　energy　criterion.　An　application　assuming　a　compressible　Mooney-Rivlin　material　is　performed.　The　equilibrium　solutions　for　the　case　of　vertical　load　present　primary　and　secondary　branches.　Although,　the　stability　analysis　reveals　that　the　only　form　of　instability　is　the　snap-through　phenomenon.　Finally,　the　finite　theory　is　linearized　by　introducing　the　hypotheses　of　small　displacement　and　strain　fields.　By　doing　so,　the　classical　solution　of　the　two-bar　truss　in　linear　elasticity　is　recovered.　©　2019,　Springer　Nature　B.V.