In　this　paper,　static　and　dynamic　stability　analyses　taking　axial　excitation　into　account　are　presented　for　a　laminated　carbon　fiber　reinforced　polymer　(CFRP)　cylindrical　shell　under　a　non-normal　boundary　condition.　The　non-normal　boundary　condition　is　put　forward　to　signify　that　both　ends　of　the　cylindrical　shell　are　free　and　one　generatrix　of　the　shell　is　clamped.　The　partial　differential　motion　governing　the　equations　of　the　laminated　CFRP　cylindrical　shell　with　a　non-normal　boundary　condition　is　derived　using　the　Hamilton　principle,　nonlinear　von-Karman　relationships　and　first-order　deformation　shell　theory.　Then,　nonlinear,　two-freedom,　ordinary　differential　equations　on　the　radial　displacement　of　the　cylindrical　shell　are　obtained　utilizing　Galerkin　method.　The　Newton-Raphson　method　is　applied　to　numerically　solve　the　equilibrium　point.　The　stability　of　the　equilibrium　point　is　determined　by　analyzing　the　eigenvalue　of　the　Jacobian　matrix.　The　solution　of　the　Mathieu　equation　describes　the　dynamic　unstable　behavior　of　the　CFRP　laminated　cylindrical　shells.　The　unstable　regions　are　determined　using　the　Bolotin　method.　The　influences　of　the　radial　line　load,　the　ratio　of　radius　to　thickness,　the　ratio　of　length　to　thickness,　the　number　of　layers　and　the　temperature　field　of　the　laminated　CFRP　cylindrical　shell　on　static　and　dynamic　stability　are　investigated.