The long-term extreme pressure in the membrane LNG tank and structural response of the Mark III containment system are addressed. The effect of hull slamming-induced vibrations on the vertical acceleration is investigated and found to be important in certain situations. Determining structural response due to sloshing requires a stepwise approach considering long-term variation of the sea state, ship motion in a stochastic seaway, fluid motion in the tanks, pressures acting on the tank structure, structural load effects, and their comparison with the appropriate resistance. This paper is focused on the determination of the critical conditions to limit the number of combinations of sea states, vessel heading, and speed that need to be considered in estimating extreme sloshing pressures. In this context, an approximate method is introduced and validated. These sea states are determined by a full linear long-term analysis. The response quantiles suitable for the contour line approach are also found using simplified criteria. The effect of avoiding heavy weather in vessel operation on sloshing and whipping-induced pressures is investigated. Sloshing experiments and various scaling approaches are described. Application of the generalized Pareto distribution and correctly determining its shape parameter is discussed. Structural response of the LNG membrane tank wall is investigated. The importance of accounting for the steel flexibility in calculating sloshing response is shown. A new method for approximating the time history of sloshing impact pressure is suggested.