Periodic　solutions　and　numerical　simulations　for　a　composite　laminated　circular　cylindrical　shell　under　the　parametric　excitation　of　temperature　are　investigated　in　this　paper.　By　introducing　some　transformations　and　defining　a　Poincaré　displacement　map,　some　results,　including　the　existence　condition　for　periodic　solutions,　least　upper　bound　of　the　number　of　periodic　solutions　and　the　parameter　control　conditions,　are　obtained.　To　demonstrate　the　applicability　and　validity　of　our　theoretical　results,　the　phase　portraits　of　the　periodic　solutions　with　different　values　of　the　detuning　parameter　are　presented　by　numerical　simulations.　©　Published　under　licence　by　IOP　Publishing　Ltd.