In　this　paper,　a　cylinder　contact　model　with　different　axis　crossing　angles　is　proposed,　and　the　axis　crossing　angle　is　introduced　into　the　normal　and　tangential　constitutive　equations.　This　paper　uses　the　method　of　formula　derivation　to　establish　the　analytical　solution　of　the　tangential　elastic　contact　of　the　cylinder　with　different　axis　cross　angles,　and　gives　the　relational　expression　of　the　tangential　load　and　the　tangential　displacement.　The　finite　element　method　(FEM)　is　used　to　verify　the　tangential　displacement　load　curve　and　the　tangential　stiffness　curve　of　the　two　cylinders.　The　influence　of　various　factors　on　mechanical　properties　such　as　tangential　stiffness,　tangential　displacement　and　contact　area　is　explored,　and　the　distribution　of　stress　and　strain　on　the　contact　surface　is　analyzed.　The　research　results　show　that　the　tangential　displacement　and　tangential　stiffness　of　the　cylindrical　contact　model　correspond　well　to　the　simulation　results.