The　investigation　of　the　mechanical　properties　of　contact　surfaces　under　tangential　cyclic　loading　is　very　important　for　understanding　the　stiffness　and　damping　of　combined　structures.　In　this　paper,　using　Hertzian　contact　theory　and　Coulomb＇s　friction　law,　the　contact　mechanical　mechanism　of　a　common　cosine　cylindrical　contact　model　subjected　to　tangential　loading,　unloading,　and　reloading　is　investigated,　and　the　load-displacement　curves　(hysteresis　curves)　and　the　energy　equations　of　a　complete　displacement　cycle　are　deduced.　The　results　show　that　under　the　action　of　tangential　cyclic　load,　the　shear　stress　increases　immediately,　and　the　micro　slip　zone　outside　the　contact　area　gradually　expands　inward　until　it　becomes　a　slip　zone.　At　this　point,　the　hysteresis　curve　changes　from　a　＇shuttle　shaped＇　to　a　＇quadrilateral＇　shape.　In　addition,　nonlinear　finite　elements　are　used　for　static　simulation　to　verify　the　accuracy　of　the　hysteresis　curve,　tangential　stiffness,　and　energy　dissipation　analysis　of　the　cosine　contact　model　under　different　axial　crossing　angles.　The　energy　equation＇s　fluctuation　with　tangential　displacement　under　different　conditions,　as　well　as　the　impact　of　friction　coefficient,　axial　intersection　angle　of　the　contact　surface,　external　load,　and　cosine　surface　characteristics　on　the　mechanical　properties　of　the　contact　surface.　With　the　increase　of　surface　roughness　or　normal　load,　energy　increases　nonlinearly　with　the　increase　of　displacement.　Finally,　when　the　Von　Mises　stress　reaches　the　yield　limit,　reciprocating　displacement　loading　will　lead　to　plastic　accumulation,　resulting　in　wear　and　tear.