The lightweight of liquefied natural gas (LNG) tanker can reduce transportation cost and improve transportation efficiency. However, in lightweight design, the random vibration analysis based on fluid–structure interaction (FSI) is difficult, which demands to be effectively solved by simplifying the finite element model and load. The vibration test and fluid–structure interaction modal numerical analysis of a tanker model were carried out, respectively, and the results are in good agreement. Taking the DC18 LNG tanker as an example, the random vibration response analysis was carried out based on the fluid–structure interaction modal numerical analysis, and the random fatigue damage coefficient of the support region of the inner container was obtained, which was used as the benchmark for the model and load simplification. The finite element model of the LNG tanker was simplified by applying the equivalent liquid mass to the walls of the inner container in the form of density. It is found that when the equivalent liquid mass ratio is 40%, the random vibration response characteristics of the DC18 LNG tanker are close to the actual structure. In the static calculation of the simplified model, the stress response of the container support area is close to the actual structural when the equivalent road spectrum load is 0.95 g vertical acceleration. In this case, the stress result and the overall damage coefficient equivalent to the actual structure can be obtained just by static calculation, which greatly simplifies the solution process.