Thin-walled cylindrical shell structures are widely used in various engineering fields due to their highly efficient load carrying capacity. This kind of structures is prone to buckling failure when subjected to axial compression loads. Machining the shell into corrugated shape is an effective method to prevent buckling. Rational design of corrugated shells can improve the load carrying efficiency of shell structures. However, there are few studies focused on the effects of various parameters on the longitudinal corrugated cylindrical shell buckling. In this paper, numerical studies are performed to analyze the factors affecting the buckling behaviors of thin-walled longitudinal corrugated cylindrical shells under axial compression loads. The cross section of the corrugated shell is obtained by superposing the sine curve on the reference circle. The critical buckling load, buckling mode and imperfection sensitivity of the longitudinal corrugated cylindrical shells are examined and compared with ordinary cylindrical shells. The effects of shell dimensions and material yield strength are taken into account. In addition, the influence of cross section shape parameters on the critical buckling load is considered, including the amplitude A and wave number k. Results show that the axial load carrying capacity of longitudinal corrugated cylindrical shells is better than ordinary cylindrical shells, and rational design of cross section shape can enhance the stability of corrugated shells. This work can provide some reference for relevant experimental studies. Furthermore, it can also give some guides for the application of thin-walled longitudinal corrugated cylindrical shells in actual engineering.