It　is　very　important　to　establish　a　constitutive　model　for　the　dynamic　response　of　rubber　structure.　Dynamic　testing　of　disc　rubber　samples　was　carried　out　by　dynamic　thermomechanical　analysis　(DMA),　obtaining　experimental　data　of　rubber　dynamic　response.　Based　on　the　superposition　property　of　WORKBENCH　constitutive　model,　a　hyperelastic-viscoelastic　constitutive　model　was　established,　in　which　the　superelastic　model　characterizes　the　large　deformation　of　rubber　and　the　viscoelastic　model　characterizes　the　hysteresis　effect　of　the　rubber.　Using　the　empirical　formula,　the　parameters　of　the　hyperelastic　model　were　identified,　and　using　the　relaxation　curve　obtained　by　the　DMA　experiment　through　the　ANSYS　viscoelastic　parameter　fitting　channel,　the　viscoelastic　model　parameters　were　identified.　Establishing　the　simulation　model　consistent　with　the　experimental　conditions,　the　error　between　experimental　data　and　simulation　data　is　small　and　within　a　reasonable　range.　The　correctness　of　the　established　hyperelastic-viscoelastic　constitutive　model　was　verified.　The　response　characteristics　of　the　disc-shaped　rubber　specimen　and　the　cubic　rubber　specimen　under　the　cyclic　torsional　load　and　vertical　load　were　obtained,　respectively.　The　applicability　of　the　constitutive　model　was　also　verified.　The　dynamic　response　characteristics　of　the　cubic　rubber　specimens　in　the　hyperelastic-viscoelastic　constitutive　model,　linear　bomb-viscoelastic　constitutive　model　and　single　hyperelastic　bomb　constitutive　model　show　that　the　constitutive　model　has　the　best　response　to　the　dynamic　response　of　the　rubber　structure.　It　provides　a　reference　for　the　selection　of　rubber　constructive　models　in　engineering　practical　problems.　©　2019,　Editorial　Department　of　Journal　of　Beijing　University　of　Technology.　All　right　reserved.