With advancements in semiconductor manufacturing processes and the development of precision processing technology, flexure hinge-based ultra-precision positioning stages are widely used. In the flexure hinge, axial and bending stiffness properties greatly influence positioning performance. This study examined the stiffness properties of elliptic and parabolic 2-degrees-of-freedom (DOF) hinges, which have not been extensively discussed. The Timoshenko beam theory was applied to derive the stiffness equations for the axial and bending directions of each hinge. The stiffness properties were examined in several design conditions by comparing theoretical and finite element analyses. Based on the results of the analyses, an empirical formula in exponential form for the design of an elliptic hinge was constructed through surface-fitting. The elliptic hinge was found to be a better alternative to a circular hinge under certain design conditions by adjusting two design parameters. In the future, we will develop sophisticatedly designed hinges with improved axial and bending stiffness properties compared to the existing circular and elliptic hinges.