Flexure hinges inherently lose stiffness in supporting directions when deflected. In this paper a method is presented for optimizing the geometry of flexure hinges, which aims at maximizing supporting stiffnesses. In addition, the new -flexure hinge design is presented. The considered hinges are subjected to a load and deflected an angle of up to ±20 deg. The measure of performance is defined by the first unwanted natural frequency, which is closely related to the supporting stiffnesses. During the optimization, constraints are applied to the actuation moment and the maximum occurring stress. Evaluations of a curved hinge flexure, cross revolute hinge, butterfly flexure hinge, two cross flexure hinge types, and the new -flexure hinge are presented. Each of these hinge types is described by a parameterized geometric model. A flexible multibody modeling approach is used for efficient modeling while it accounts for the nonlinear geometric behavior of the stiffnesses. The numerical efficiency of this model is very beneficial for the design optimization. The obtained optimal hinge designs are validated with a finite element model and show good agreement. The optimizations show that a significant increase in supporting stiffness, with respect to the conventional cross flexure hinge, can be achieved with the -flexure hinge.