The energy expressions are formulated for the axially stiffened shell treating the stiffeners as discrete elements. The principle of minimum potential energy is employed to formulate the buckling equations for a simply supported, axially stiffened shell under uniform axial compression. The displacement functions are expended into double trigonometric series. The mode assuming method employed in this paper makes it possible to reduce the matrix size of the eigenvalue problem considerably. Effects are made to investigate the transition from overall buckling to local buckling and to verify the existence of the minimum stiffness ratio of stiffener as in the case of stiffened plate. The results of the calculation show that the critical stiffener size increase linearly as the length of the shell increases. The results also show that the overall buckling load decreases and the local buckling load has a nearly constant value as the length of the shell increases. The results show very good agreements with other computational available.