Abstract: Based on the principle of synchronous radiation focusing mirror, a bending mechanism was designed, the design theory of the bending mechanism was introduced, and the calculation process of the theoretical shape of the bending mirror was deduced.Meanwhile, according to the design theory, the model of the bending mechanism based on flexible hinge was established, and its parameters were calculated, the effective length was 84.9 mm and the maximum torque was 259.8×10^-3 N·m.Furthermore, the design and check of the bending mechanism were completed, showing that the material mechanics requirements of the bending mechanism could be meet. Finally, according to the error of the theoretical surface shape error, how different factors affect the variation of the surface error was analyzed by comparing the theoretical value of the bent mirror shape with the finite element simulation value.