Abstarct: In this thesis, an analytical method is presented to investigate the nonlinear vibration behavior of the spiral stiffened functionally graded cylindrical shells surrounded by a nonlinear viscoelastic foundation exposed to the external and parametric excitations. These loads are applied radially on the surface of the shell and axially on the two edges of the cylindrical shell. The boundary condition is assumed simply supported. The nonlinear viscoelastic foundation consists of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness and viscose damping. The strain-displacement relations and the governing equations are obtained baxsed on the von Kármán nonlinear equations and the classical shells theory, respectively. The smeared stiffener technique is used to model the stiffeners on the shell. To obtain the discretized motion equation, the Galerkin method is used. In order to investigate the response of the nonlinear vibration, the multiple scales method is utilized. In this regard, at first, neglecting the internal resonance, the resonance analyses consist of primary, superharmonic, subharmonic, combination, and simultaneous resonances for the spiral stiffened functionally graded cylindrical shell with or without the initial imperfection surrounded by a nonlinear viscoelastic foundation exposed to the external excitation baxsed on the single-mode are performed. In continue, the free nonlinear vibrations and forced nonlinear vibrations with the assumption of internal resonance and one of the subharmonic or superharmonic resonances are analyzed for the cylindrical shell. So, in this case, baxsed on the proposed multi modes, after finding the stress function from the compatibility equation and substituting outcome in the motion equation of the shell, by applying the Galerkin method, the equations system with coupled modes is obtained. Also, the cylindrical shell, in addition to external excitation, is subjected to axial loading as a parametric excitation, in which case, assuming one of the resonance cases and considering the initial imperfection, the nonlinear vibrations behavior of the shell is examined. In this part, the deflection is considered baxsed on the first three prominent modes, and consequently, three equations with coupled modes are obtained. To analyze the nonlinear vibrations of the cylindrical shell with one of the resonance cases, the bifurcation diagram is depicted for the excitation frequency versus the amplitude. According to these diagrams, it is observed that the chaotic motion occurs for the spiral stiffened functionally graded cylindrical shell. The effects of different angles of stiffeners, various geometrical characteristics, and nonlinear viscoelastic foundation are investigated.