In　this　paper,　we　are　concerned　with　periodic　motions　of　composite　laminated　circular　cylindrical　shell　with　1:2　internal　resonance.　The　existence　condition　and　number　estimation　of　periodic　solutions　of　the　governing　system　are　studied　by　discussing　the　Poincaré　map　and　the　displacement　function.　To　illustrate　the　effectiveness　of　our　results,　the　method　of　numerical　simulations　is　performed　to　detect　the　phase　portraits　of　the　periodic　solutions　under　a　set　of　parameter　condition.　©　Published　under　licence　by　IOP　Publishing　Ltd.