This study aims to plan the increase of the buckling capacity on thin-walled steel cylindrical shells with stiffeners of folded and curved grooves due to pure axial compression. Then, in order to investigate the effect of the buckling capacity for thin-walled steel cylindrical shells with folded and curved grooves, the exact buckling behaviors are generated by using the original transfer matrix method. Each transfer matrix is obtained from differential equation for shell-panel or plate-panel to axial load, and the transfer equations are proposed by considering compatibility and equilibrium conditions between shell-panel and groove for cylindrical shell with folded and curved grooves. So as to study the accuracy and the efficiency of this original transfer matrix method, some numerical... examples are presented. An analytical load and overall elastic buckling loads of a steel cylindrical shell with folded and curved grooves can be obtained simultaneously. Furthermore, a technique to estimate the buckling mode shapes of a steel cylindrical shell with folded and curved grooves is also shown. Result of this study revealed that the buckling capacity of cylindrical shell with folded grooves reduce in comparison with ordinary shell without stiffener, and only cylindrical shell with shell-shaped curved grooves increases the buckling capacity. And then with the object of revealing effective number and size of shell-shaped curved grooves, the investigation is generated for the buckling strength of thin-walled steel cylindrical shells with shell-shaped grooves.