In this study, the circumferential strain concentrations in cylindrical and square tubes with corrugated surfaces subjected to axial compression are studied using the finite element method. In cylindrical tubes, the yield strength σ _y , the hardening coefficient E_h of the material and the thickness t of the tube wall exert only a small influence on the strain concentration, so that the maximum circumferential strain can be approximately evaluated as a function of the wavelength 2 λ and the amplitude a of the corrugations, and the cylinder radius R . For square tubes, however, the effect of the corner radius r , the thickness t , the yield strength σ _y , and the hardening coefficient E_h on the strain concentration is comparable to that of the wavelength 2 λ and the amplitude a of the corrugations. The maximum circumferential strain increases with a decrease in the corner radius r / D , with a decrease in the thickness t , and with an increase in the ratio σ _y / E_h .