To　solve　the　problems　such　as　too　much　trial-and-error,　limited　material　being　involved　in　the　graphs　and　calculation　results　being　obviously　influenced　by　artificial　factors　and　errors　of　the　graphs　in　the　design　of　external　pressure　vessel　according　to　current　standard　ASME　VIII-1,　GB150　and　EN13445,　the　mathematic　expression　of　the　graphic　charts　is　examined,　and　a　set　of　analytical　equations　and　algorithms　for　the　linear　and　nonlinear　instability　of　external　pressure　vessel　are　established.　The　equation　was　applied　to　calculate　the　ultimate　buckling　pressure　of　cylinder　and　spherical　shells.　The　algorithm　here　provided　can　not　only　avoid　the　shortages　of　current　graphic　analysis　methods,　but　also　be　convenient　for　technicians　to　calculate,　which　could　enrich　and　consummate　the　graphic　charts　in　the　current　standards　and　be　useful　to　the　design　of　external　pressure　vessels　to　be　made　of　new　materials.