A　structure　of　a　cylindrical　shell　with　a　circular　plate　end　cap　is　usually　used　in　connect　different　shaft　system　and　it　is　necessary　to　estimate　the　axial　stiffness　in　order　to　analyze　the　vibration　of　the　rotor　system.　This　paper　builds　the　model　of　this　structure.　The　theoretical　solution　of　the　bending　deflection　of　the　circular　plate　and　the　cylindrical　shell　are　deduced　by　using　the　classic　theory　of　plates　and　shells,　and　the　continuity　boundary　conditions　at　the　junction　of　the　circular　plate　and　the　cylindrical　shell.　Furthermore,　the　axial　stiffness　of　the　structure　is　solved　through　considering　the　relationship　between　the　external　force-bending　deformation.　Two　different　boundary　conditions　for　the　left　side　of　the　cylindrical　shell　is　considered　and　their　axial　stiffness　varying　with　the　length　of　the　cylindrical　shell　is　calculated.　For　verification,　a　finite　element　model　of　the　structure　is　built　and　analyzed.　The　theoretical　results　fairly　coincide　with　the　finite　element　ones.