The buckling analysis of stiffened cylindrical shells by rings and stringers made of functionally graded materials subjected to axial compression loading is presented. It is assumed that the material properties vary as a power form of the thickness coordinate variable. The fundamental relations, the equilibrium and stability equations are derived using the first order shear deformation theory. Resulting equations are employed to obtain the critical buckling loads. The effects of the material properties and geometry of shell on the critical buckling loads are examined. Excellent agreement with the results in the literature indicates the correctness of the proposed closed form solution.