The most important technical issue in the shipbuilding industry regarding liquefied natural gas (LNG) carrier cargo containment systems (CCS) is securing the structural reliability of the primary barrier, which is in direct contact with the LNG. Fracture of the primary barrier by the hydrodynamic load of the LNG CCS may lead to disasters because it is difficult to implement immediate safety measures in the marine environment, unlike on land. Hence, structural reliability of the LNG membrane is the most critical issue in LNG carrier CCSs, where thin and corrugated 304L stainless steel is often used as the primary barrier to prevent repeated thermal deformation from the temperature difference during loading (−163 °C) and unloading (20 °C) of the LNG. However, plastic deformation of the 1.2 mm-thick corrugated membrane of the LNG CCS has been reported continuously owing to its vulnerability to cryogenic hydrodynamic loads. In the present study, we conducted a parametric analysis to investigate the effects of the corrugation shape as a preliminary study of the primary barrier. Finite element analysis was conducted with a simplified plate to focus on the effects of corrugation. Furthermore, a two-step validation was conducted using the above experimental results to ensure reliability of the structural analysis. The results show that optimizing the corrugation shape could ensure better structural safety than the conventional design.