A　paraboloidal　contact　model　with　different　axial　crossing　angles　is　established.　The　contact　model　is　subjected　to　a　combined　action　of　normal　and　tangential　loads.　Based　on　the　Hertzian　theory,　the　contact　states　of　the　model　under　the　action　of　the　normal　load　are　obtained　by　deriving　the　equations.　The　contact　states　include　critical　interference　values　of　the　elastic　phase,　elastoplastic　phase,　and　plastic　phase.　Under　the　action　of　the　normal　preload,　the　tangential　stiffness　of　the　contact　model　is　obtained　and　verified　by　finite　element　simulation.　Simulation　results　indicate　that　tangential　displacements　of　the　contact　model　in　the　deformation　phase　correspond　well　with　analytical　solution　equations.　Stresses　and　strains　on　the　contact　surface　are　also　investigated.　By　employing　the　proposed　contact　model,　the　effects　of　axial　crossing　angle,　friction　factor,　focal　length,　and　normal　load　on　mechanical　properties　are　investigated.　The　paraboloidal　contact　model　is　advantageous　to　contact　analysis　for　paraboloidal　gears　and　cams.