In　this　article,　a　series　of　analysis　were　performed　on　a　two-dimensional　structure　of　steel　and　rubber-covered　rollers.　First,　a　hyperelastic-viscoelastic　composite　constitutive　model　based　on　a　dynamic　mechanical　experiment　of　rubber　was　formulated　to　accurately　describe　rubber　properties.　Meanwhile,　a　hyperelastic　constitutive　model　not　considering　viscoelasticity　was　set　as　the　control　group.　The　material　used　in　this　article　was　the　nitrile　rubber　with　the　Shore　hardness　of　40.　Then,　the　effects　of　viscoelasticity　on　the　von　Mises　stress　were　analyzed　by　comparing　results　of　two　models.　The　influences　of　working　conditions　(roller　speeds/compression　displacement)　on　the　von　Mises　stress　and　the　area　of　hysteresis　loop　were　also　studied.　Next,　the　contact　characteristics　under　different　working　conditions　and　constitutive　models　were　analyzed　combining　viscoelasticity.　A　verification　experiment　of　contact　width　was　carried　out,　and　the　theoretical　and　simulated　values　were　calculated　and　compared.　Finally,　the　relation　of　＂low　peak＂　phenomenon　with　viscoelasticity　was　studied,　and　the　effects　of　working　conditions　and　rubber　viscoelasticity　on　contact　feature　of　rollers　were　summarized.　The　conclusions　of　the　article　can　help　engineers　to　better　optimize　dynamic　working　conditions　and　judge　the　working　state　of　the　structure.