Considering　compressed　thin　wall　cylindrical　shell　structures　widely　used　in　aerospace　engineering,　analytic　method　and　eigenvalue　buckling　finite　element　method　are　applied　in　the　paper　to　analyze　the　stability　of　cylindrical　shell　structure　under　uniform　axial　compression,　and　the　critical　buckling　loads　respectively　are　obtained　and　contrasted　to　conclude　that　the　finite　element　model　is　reasonable.　Linear　buckling　eigenvalue　finite　element　method　is　also　employed　to　analyze　the　stability　of　cylindrical　shell　irradiated　by　intensive　laser　beam,　and　the　analysis　results　investigate　that　laser　irradiation　brings　on　high　temperature　of　local　shell　structure　and　subsequently　changes　of　material　parameter,　because　laser　irradiation　leads　to　thermal　stress　and　thermal　strain,　and　makes　me　buckling　load　of　compressed　cylindrical　shell　come　down　drastically.　The　stability　of　stiffened　cylindrical　shell　structure　is　focused　to　be　studied　as　well,　and　numerical　analysis　results　indicate　that　stiffeners　are　valid　to　improve　the　capability　of　compressed　shell　and　more　effective　under　combined　function　of　axial　compression　and　laser　irradiation.