Deep-notch elliptical flexure hinges are more suitable for a flexible mechanism with large stroke requirements as compared with other common flexure hinges, so this paper optimizes their design. The stiffness model of deep-notch elliptical flexure hinges was established firstly, and the impact of structural parameters on the rotational stiffness was also discussed in detail. Then, the flexibility matrix was analyzed by using Newton-cotes quadrature formula to simplify the calculation of flexibility coefficients, and each structural parameter was optimized by fuzzy optimization method based on the multi-objective optimization model. The results of optimization show that the angular displacement rotated with the Z axis is improved by 16.72%, while that rotated with the Y axis is decreased by 16.01%, and the linear displacements along the axes X, Y, Z are decreased by 10%, 2933% and 51.84%, respectively. After optimization, the rotation capacity of Z axis has been improved and the transmission capacities in other directions are both inhibited, so that the movement accuracy and structural flexibility are enhanced. The test results demonstrate that the optimized deep-notch elliptical flexure hinges meet the requirements of high-precision and large travel of waveguide package positioning platforms.