Elastomers　are　typically　considered　incompressible　or　slightly　compressible.　However,　we　present　simple　tension　and　bulk　tests　showing　that,　under　large　deformations,　these　materials　can　undergo　significant　volume　changes.　A　review　of　the　literature　reveals　the　lack　of　an　accurate　hyperelastic　model　for　finite　volumetric　deformations　of　elastomers.　Therefore,　we　propose　a　new　volumetric　strain　energy　density　(SED)　that　overcomes　the　limitations　of　the　current　models.　The　main　advantages　of　the　proposed　SED　are:　(1)　accurate　description　of　the　response　of　rubbers　for　both　small　and　large　volumetric　deformations;　(2)　ability　to　reproduce　diverse　behaviors　during　volume　shrinkage　and　expansion;　(3)　adaptability　to　other　compressible　materials,　such　as　soft　tissues,　foams　and　hydrogels.　Using　the　deviatoric–volumetric　split　of　the　strain　energy,　the　proposed　volumetric　SED　is　combined　with　a　suitable　deviatoric　part　selected　from　the　literature.　The　parameters　of　the　combined　SED　are　calibrated　by　fitting　the　model　to　the　experimental　data　from　simple　tension　and　bulk　tests.　As　a　result,　an　accurate　description　of　the　response　of　elastomers　under　both　shape　and　volume　deformations　is　provided.　The　proposed　SED　can　be　implemented　in　numerical　codes　to　capture　the　effects　of　volumetric　deformations　on　the　equilibrium　solutions　for　various　stress　states.　©　2023　Elsevier　Ltd