Buckling analyses of heavily corrugated cylindrical shells based on detailed full finite element models are usually computationally expensive. To address this issue, we have pro- posed an efficient computational method of predicting the onset of buckling for corrugated cylindrical shells which builds on the Bloch wave method for infinitely periodic structures. We modified the traditional Bloch wave method in order to analyze the buckling of rotationally periodic shell structures. We have developed an efficient algorithm to perform our modified Bloch wave method. The buckling behavior of composite corrugated cylindrical shells with a range of numbers of corrugations was analyzed. Linear and nonlinear buckling analyses of detailed full finite element models were also performed and compared to our method. Comparisons showed that our modified Bloch wave method was able to obtain highly accurate buckling loads and it was able to capture both global and local buckling modes. It was also found that the computational time required by our modified Bloch wave method did not scale up as the number of corrugations increased.