This paper investigates the buckling behavior of steel cylindrical silos with corrugated walls and vertical stringers under axial compression. The study integrates analytical, numerical, and statistical analyses to understand the influence of geometrical parameters such as radius, wall thickness, and corrugation profile on the buckling phenomenon. The analytical calculations elucidate the critical buckling load for various scenarios, considering both unstiffened and stiffened wall configurations. The finite element analysis provides numerical validation, while the statistical analysis offers insights into the sensitivity of the critical buckling load to different parameters. The results highlight the significance of corrugation height and suggest the optimal design parameters for maximizing buckling resistance while minimizing structural weight.