The postbuckling behavior of a circular cylindrical shell subjected to axial compression is considered. Because of numerical difficulties, previous analyses of this problem have been severely restricted and do not yield quantitatively satisfactory results. The most accurate such analysis gives a minimum postbuckling load that is approximately three times higher than corresponding test values. In the present analysis, the number of free constants in the displacement function has been considerably increased, and the computed minimum postbuckling load is in close agreement with available test results. Additional tests are suggested to support the establishment of a buckling criterion which, together with the presently computed postbuckling curve, could serve as a sound basis for the design of cylinders under axial compression. (Author).