In design process of the LNG (liquefied natural gas) CCS (cargo containment systems), it is very difficult to determine the effects of sloshing impact and the corresponding response of the CCS. The reliable sloshing assessment methods for LNG CCS are important to satisfy the structural strength of the systems. Since compressibility of the sloshing impact may limit the maximum pressure, mixture model of multiphase is required to represent the sloshing physics. A multiphase CFD model has been introduced to simulate the impact of the LNG sloshing by considering the two phases of gas and liquid. The scheme of CFD model is tried based on the Eulerian domain model that employs the CVFEM. It includes the interphase momentum interaction between liquid and gas. For verification of numerical model, sloshing impact in a rectangular insulation box is simulated to compare the sloshing impacts induced by inhomogeneous multiphase model. Also, the numerical model is applied to localized FSI model for strength assessment of LNG CCS.