Liquefied Natural Gas (LNG) Cargo Containment Systems (CCSs) are representative complex systems used in energy and transportation industries. Usually, a structural combination of double barriers and two-layer thermal insulation panels is used for a membrane-type CCS system. In such a system, the primary barrier is made of 1.2-mm thick austenitic stainless steel having a crossed-corrugated shape. In the design and fabrication stage, the primary barrier should be handled with care in order to prevent structural defects, because structural defects may induce LNG leakage and catastrophic failure of the entire system. During the loading and unloading of LNG, several types of structural components may fall onto the CCS from an immense height. However, realistic failure examples are not enough to explore the failure mechanism. In this study, falling-object-induced structural failure of the primary barrier in membrane-type LNG CCS systems was evaluated. To represent falling objects of varied shapes, cylindrical, dihedral, and trihedral impactors were considered. Failure mechanisms, such as penetration, are examined based on the test scenario. In order to secure a wider application of the finite element analysis (FEA) technique as a design-aid numerical method, intensive comparisons of FEA results and experimental observations were carried out. As a key factor in the FEA, we suggest the Johnson–Cook parameter, which can be applied to the dynamic failure problem for curvature steel plates used in LNG CCS membranes. It was experimentally verified that the full consideration of stress triaxiality in the J–C model might improve the numerical method.