Decarbonization plays an important role in future energy systems for establishing a zero-carbon society. Hydrogen is believed to be a promising energy source that can be converted, stored, and utilized efficiently, leading to a broad range of possibilities for future applications. Hydrogen can be stored in various forms, including compressed gas, liquid hydrogen, hydrides, adsorbed hydrogen. Among these, liquid hydrogen has high gravimetric and volumetric hydrogen densities. There are a lot of previous studies on thermal behavior of MLI and VCS and optimization insulation system, but research on the insulation performance by varying the head shape of the tank has not been conducted. In this study, thermal-structural coupled analysis was conducted on the insulation system with VCS positioned between two layers of MLI for a liquid hydrogen storage tank. The analysis considered dome shapes (torispherical, circle, ellipses), and heat flux and temperature were derived from thermal analysis to predict insulation performance. Maximum equivalent stress and deformation were calculated from the structural analysis, and the optimal dome shape was proposed.