In order to solve the buckling problem of the flexure hinge in flexible microgripper caused by alternating stress, the circular notch flexure hinge was taken as an example for force analysis under the working load, and the calculation formula of the critical force was derived. The finite element buckling analysis of the hinge was performed by using Ansys Workbench 17.0, the firstorder buckling mode was obtained, and compared with the critical force obtained by using the derived formula, the error was 0.23%. The accuracy of the formula was verified. Orthogonal experimental design was introduced to find out the controllable factors and noise factors affecting the critical force, and the orthogonal experimental design was carried out. The weight analysis method was used to quantitatively analyze the influence degree of parameters on the critical force. The results show that the weight of each parameter on the change of critical force is different, which provides a theoretical basis for hinge design.