Careful and numerical analysis eccentrically stiffened shells in the industry is a major step forward in the design of these shells. In this paper, a careful analysis of post-buckling behavior of eccentrically stiffened FGM thin circular cylindrical shells is surrounded by an elastic foundation and external pressure is presented. The two parameter elastic foundation based on Winkler and Pasternak elastic model is assumed. Stringer and ring stiffeners are internal. Shell properties and eccentrically stiffened are FGM. Fundamental relations and equilibrium equations are derived based on the smeared stiffeners technique and the classical theory of shells and according to von- Karman nonlinear equations. The three-term approximation for the deflection shape, including the pre-buckling, linear buckling shape and nonlinear buckling shape was chosen that using the Galerkin method, the critical load and post-buckling pressure-deflection curves is calculated. The effects of different dimensional parameters, buckling modes, volume fraction index and number of stiffeners are 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.