In recent years, there has been a demand for the large-scale membrane type LNGC due to the energy crisis. The cargo containment system (CCS) attached to the LNGC cargo tank is directly exposed to the sloshing load. Different pressure distribution forms may cause different failure modes of insulation box. The separate analysis of a single component or a single failure form cannot fully reflect the strength of CCS. Besides, the traditional numerical model with single insulation box and simply supported condition may overestimate the strength. In this study, a refined CCS numerical model attached to the inner hull structure is proposed. The deformed hull structure under sloshing impact is taken as the flexible boundary condition of CCS. The ultimate shear, bending, crushing and buckling strengths of NO96 CCS are assessed under various structures and boundary conditions. Finally, the multimode coupled analysis is conducted to fully assess the failure of CCS. The results show that the increase of structural stiffnesses can directly improve the ultimate strength. The weak structural and supporting stiffnesses make the buckling failure of insulation box become the most dangerous failure mode. The support from the strong hull structure leads to the shear failure of primary bottom plate. In the rest of loading conditions, the bending failure of primary horizontal plates need to be focused.