Abstract: Cryogenic flexible hose is one of the core equipment for transporting liquefied natural gas in the floating liquefied natural gas (FLNG) system. As the inner layer of LNG cryogenic flexible hose, U-shaped bellow directly affects the mechanical properties of the LNG cryogenic flexible hose. In this paper, the wave diameter and ring plate length are selected as independent structural design parameters for structural analysis, which solves the coupling calculation problem that the wave height changes with the change of wave distance in the traditional U-shaped bellows sensitivity analysis. The radial basis function neural network surrogate model is constructed, and the genetic algorithm is used to carry out the multi-objective optimization of the U-shaped bellows structure. The Pareto optimal solution set with the maximum tensile stiffness and the minimum bending stiffness as the optimization objectives is obtained, which provides a useful reference for the design of U-shaped bellows in practical engineering applications.