In this paper, the authors test a method of studying the stability and stress-strain state of a cylindrical shell structure under various loads in the ANSYS Mechanical APDL 19.2 software package. The analyses are performed using the arc-length method. Shell 181 is chosen as an element type, which makes it possible to account for large strains during the analyses. The shells have fixed-pin joints on two sides and a free edge on the other two sides. A concentrated force and a uniformly distributed load are considered as load cases. Normal displacement vs. load graphs are obtained for all options of the structures considered; the values are calculated with account for geometric nonlinearity. Buckling load values are obtained for various options of structures with a uniformly distributed load, the other structures remain stable. A significant difference in critical values as compared to the linear analysis indicates the need for taking into account geometric nonlinearity.