An optimization design method for elliptical flexure hinges is researched. As the traditional calculation formula for the stiffness of elliptical flexure hinges is more complex, this paper deduces a approximate theoretical formula by nonlinear fitting method with power function. Based on the approximate theoretical formula, it analyzes the precision characteristics of the flexure hinges and their maximum stresses at working. Then, the global optimization solver GlobalSearch and local optimization solver Fmincon are used to design optimally the maximum stiffness of an elliptical flexure hinge at a working direction. Finally, the applicability of the approximate theoretical calculation equation and the accuracy of the optimization results are assessed by comparison with the results from finite element analysis and experimental data. The results show that the relative errors between the finite element simulation, experimental data and the approximate theoretical calculation for the stiffness of elliptic hinge are within 5%. It concludes that the method avoids establishing the complex finite element mode and the processes of calculation and modification, and greatly improves the design efficiency. Moreover, it can obtain the maximum stiffness of the elliptical flexure hinges by optimization calculation.