The sandwich panels are elements of launch vehicles and autonomous aerospace vehicles. The buckling of cylindrical sandwich panels with imperfections is considered. The core layer of such panel is a honeycomb structure made from polylactide (PLA) material and manufactured by fused deposition modeling (FDM) additive technology. The inner and outer panel layers are made of carbon fiber-reinforced materials. The purpose of this work is determination the effect of cell breakings on the buckling cylindrical sandwich panels with imperfections under longitudinal compression and radial pressures. This will make possible to use some sandwich panels with imperfections in the production. The scientific novelty of this study is the following. The influence of honeycomb imperfections in the form of cell breakings on the critical buckling modes is studied. Eight cases of imperfection patterns, in terms of numbers and locations of the cell breakings, are considered. Numerical computations show that the sandwich panels under longitudinal compression are moderately sensitive to imperfections, with decreases in critical load ranging from 5.3% for a single cell breaking in the center of the honeycomb to 8.6% for multiple cell breakings located along different directions. Also, the corresponding buckling mode is global. In contrast, the buckling behavior of sandwich panels subject to radial pressure is highly sensitive to imperfections, such that the presence of a single cell breaking results in a critical load more than three times smaller than that of the perfect panel. The results on cell breakings influence on the shell buckling can be used for thin-walled structure design.