The longitudinal compressive buckling of long and thin-walled cylinders in yield region was analyzed with the incremental and finite forms of the endochronic constitutive equation respectively. The relations between the critical stress and the ratio of R(the radius)/h(the thickness of the wal) were derived. The critical stresses of thin-walled cylinders made from aluminum alloys were analyzed and compared with the experimental data. It was found that in most cases, both forms of the endochronic constitutive equation provide more satisfactory results.