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This paper treats the problem of determining the Critical stress in the case of axial compressin of a circular cylindrical shell. We solved this problem according to the total potential energy method, then we obtain for [numerical formula] equation (10). We shall try to determine the additional displacement components in the form (12), using (2)〜(4), introducing (12) in equation (10) we obtain the relationship (16) between the axial stress and the shell parameters, the numbers of waves m and n on the circumference and axis with the buckling of the shell. This form is different from the other solution (16') by W. Flugger and Timoshenko, that we take the non-linear expressional equation (2), (3) between the relative elongations, the bending deformations and the displacement.