In　this　paper,　the　radial　nonlinear　vibrations　are　investigated　for　a　thin-walled　hyperelastic　cylindrical　shell　composed　of　the　classical　incompressible　Mooney-Rivlin　materials　subjected　to　a　radial　harmonic　excitation.　Using　Lagrange　equation,　Donnell＇s　nonlinear　shallow-shell　theory　and　small　strain　assumption,　the　nonlinear　differential　governing　equation　of　motion　is　obtained　for　the　incompressible　Mooney-Rivlin　material　thin-walled　hyperelastic　cylindrical　shell.　The　differential　governing　equation　of　motion　is　simplified　to　a　generalized　Duffing　equation　with　the　quadratic　term.　The　second-order　approximate　analytical　solutions　are　obtained　by　using　the　modified　Lindstedt-Poincare　(MLP)　method.　The　impacts　of　the　parameters　on　the　amplitude-frequency　response　curves　and　number　of　the　equilibrium　points　are　analyzed.　According　to　Runge-Kutta　method,　the　bifurcation　diagrams,　Lyapunov　exponents　and　Poincare　maps　are　obtained.　The　chaotic　behaviors　are　found　in　the　radial　nonlinear　vibrations　of　the　incompressible　Mooney-Rivlin　material　thin-walled　hyperelastic　cylindrical　shell.　The　results　demonstrate　that　the　nonlinear　dynamic　responses　of　the　incompressible　Mooney-Rivlin　material　thin-walled　hyperelastic　cylindrical　shell　are　highly　sensitive　to　the　structural　parameters　and　external　excitation.