For the flexible hinge of compliant mechanism under the action of alternating symmetrical cyclic load, the stress concentration in the weakest area of the flexible hinge is easy to cause, resulting in the fatigue failure of the flexure hinge，taking the elliptical flexible hinges in compliant mechanisms as the research object, based on the theory of pure bending in material mechanics, the calculation formula of maximum concentrated stress at the notch of an elliptical flexure hinge is derived. By using the ANSYS software, the accuracy and feasibility of the calculation formula are verified. On this basis, by introducing linear regression method, the life prediction model of elliptical flexure hinge is established, which can predict the fatigue life of elliptical flexure hinge and solve the fatigue failure problem. Finally, an example is given to verify the correctness and effectiveness of the model, an important reference for fatigue failure and life prediction of other types of flexure hinges is provided.