Compliant mechanisms have many advantages over rigid-link mechanisms. However, one of the challenges of compliant mechanisms is the trade-off between a large range of motion and a high out-of-plane stiffness. Furthermore, the out-of-plane stiffness is shown to vary over the range of motion. Especially for large-displacement compliant mechanisms this can be by a significant amount. In this paper the use of curved beam elements in a compliant mechanism is shown to have impact on this tradeoff. The influence of curved beam elements on the out-of-plane stiffness over the entire range of motion is presented for simple structures such as a single beam element and double beam elements, as well as a compliant finger. With the use of a genetic algorithm optimization, the difference in performance of a design with only straight beam elements versus one with curved beam elements is highlighted and the effect on the out-of-plane stiffness profile is presented. The optimization with curved beam elements results in solutions with a performance in terms of objective function values that cannot be found by the optimization with only straight beam elements. It is shown that for simple structures the use of curved beam elements has a large influence on the shape of the out-of-plane stiffness profile along the range of motion, while for the compliant finger the influence is mainly in the variables of the out-of-plane stiffness profile.