Abstarct: The eccentrically stiffened cylindrical shells are one of the most important structures in aerospace industries. Careful and numerical analysis eccentrically stiffened shells in the industry is a major step forward in the design of these shells. In this thesis, semi-analytical method for eccentrically stiffened FGM cylindrical shells with asymmetrical stiffeners and in the specific state; symmetrical stiffeners or stringer and ring stiffeners under pressure and surrounded by an elastic medium is presented. Suppose that an ES-FGM cylindrical shell is simply supported. The proposed model is baxsed on two parameter elastic foundation Winkler and Pasternak. For the dynamic analysis, non-linear elastic foundation is considered. The eccentrically stiffened are also FGM. According to the Von Karman nonlinear equations and the classical theory plate of shells, strain displacement relations are obtained. The smeared stiffeners technique and Galerkin method, used for solving nonlinear dynamic problem. With considering three terms approximation for the deflection shape, relationship of the frequency-amplitude of non-linear vibration obtained in a simple form. The nonlinear dynamic response is obtained from fourth order Runge-Kutta method.The nonlinear buckling dynamic behavior of stiffened FGM shells is investigated baxsed on the Budiansky-Roth criterion. The effect of parameters eccentrically stiffened, elastic foundation and excitation force on the curve frequency-amplitude of nonlinear vibration and the effect of damping and loading speed on the nonlinear dynamic response of cylindrical shells FGM have been investigated. The natural frequency, static and dynamic buckling load are analyzed, too. For the static, analysis he effects of different dimensional parameters, buckling modes, volume fraction index and number of stiffeners is investigated. Numerical results show that stiffeners and elastic foundation enhance the stability of the shells. Increasing the shell thickness, reducing the volume fraction index, raising the number of Stringer and ring stiffeners and applying foundation elastic, causes the critical buckling load is increased, too. The effect of different angels of stiffeners and temperature-dependent material properties on results in both of static and dynamic state has been investigated, too.