In order to solve the problems of large heat leakage and unclear stress of the adiabatic support structure in the cryogenic storage tank, a finite element model of a 37.4 m³ storage tank was established by the method of thermal-solid interaction, and the heat transfer, stress and deformation of the tank were analyzed, and the supporting structure was optimized. The results show that the daily evaporation rate of liquid nitrogen is 0.10%/d when the heat leakage through the supporting structure is 62.18 W, and the heat leakage of the supporting structure decreases with the decrease of ambient temperature. The influence of liquid temperature on the storage tank is mainly concentrated in the support structure and the inner tank, and the stress and deformation of the support structure increase greatly after considering the influence of temperature, and the maximum stress of the inner tank is less affected, and the deformation is increased by 11.81 times. When storing liquid hydrogen, the heat transfer of the support structure increases by 26% compared with liquid nitrogen. The topology of the supporting structure under the sliding end was optimized with the minimum heat transfer as the optimization goal. The heat transfer of the "Y" type support structure is reduced by 27.20% and the maximum stress is reduced by 7.73%.