The leakage of cryogenic LNG through cracks in the insulation membrane of an LNG carrier causes the hull structure to experience a cold spot as a result of the heat transfer from the LNG. The hull structure will become brittle at this cold spot and the evaporated natural gas may potentially lead to a hazard because of its flammability. This paper presents a computational model for the LNG flow and heat diffusion in an LNG insulation panel subject to leakage. The temperature distribution in the insulation panel and the speed of gas diffusion through it are simulated to assess the safety level of an LNG carrier subject that experiences a leak. The behavior of the leaked LNG is modeled using a multiphase flow that considers the mixture of liquid and gas. The simulation model considers the phase change of the LNG, gas-liquid multiphase interactions in the porous media, and accompanying rates of heat transfer. It is assumed that the NO96-GW membrane storage is composed of glass wool and plywood for the numerical simulation. In the numerical simulation, the seepage, heat diffusion, and evaporation of the LNG are investigated. It is found that the diffusion speed of the leakage is very high to accelerate the evaporation of the LNG.