In this study, the buckling behavior of optimum laminated composite cylindrical shells subjected to axial compression and external pressure are studied. The cylindrical shells are composed of multi orthotropic layers that the principal axis gets along with the shell axis (x). The number of layers and the fiber orientation of layers are selected as optimization design variables with the aim to find the optimal laminated composite cylindrical shells. The optimization procedure was formulated with the objective of finding the highest buckling pressure. The Genetic Algorithm (GA) and Imperialist Competitive Algorithm (ICA) are two optimization algorithms that are used in this optimization procedure and the results were compared. Also, the effect of materials properties on buckling behavior was analyzed and studied.