Abstract: The longitudinal compressive buckling of long and thin-walled cylinders in yield region is analyzed with the incremental and finite forms of the endochronic constitutive equation, respectively. The relations between the critical stress σ_crversus the ratio of R (the radius) versus h (the thickness of the wall) are derived. The critical stress of the thin-walled cylinders made of abuminum alloys AMГ and Д1T are analyzed and compared with the experimental data and the analytical results based on traditional theory of plasticity. It is seen that. except that the σ_cr of the cylinders made of 1Tpredicted by the finite form of the endochronic theory seems a little more conservative than that by traditional deformation theory of plasticity, in most cases, both forms of the endochornic constitutive equation provide more satisfactory results.