Flexure hinges inherently lose stiffness in supporting directions when deflected. In this paper a method is presented for optimizing the geometry of flexure hinges, while supporting stiffnesses are retained. These hinges are subjected to a load and deflected an angle of up to ±20°. The measure of performance is defined by the first unwanted eigenfrequency, 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 three cross flexure hinge types and a butterfly flexure hinge are presented. A flexible multibody modeling approach is used for efficient modeling. Each of these hinge types is described by a parameterized geometric model. The obtained optimal hinge designs are validated with a finite element model and show good agreement. The optimal solution of the butterfly flexure hinge shows the least decrease in the supporting stiffnesses of the evaluated hinges.