Cable chains are essential for guiding and protecting cables in repetitive linear-motion equipment. However, during highspeed operations, inertial effects and structural deformation can lead to position overshoot beyond the intended stroke, resulting in off-path motion and increased stress concentrations in links and joints. This study assesses the structural stability of a U-shaped cable carrier under conditions of position overshoot and suggests an optimized geometry. To analyze this, a nonlinear finite element model is employed, constraining one end of the carrier while applying a prescribed overshoot displacement to the other end. Structural stability is measured using a stability index, which is defined as the maximum reaction force at the point of yielding, when the equivalent (von Mises) stress reaches the material's yield stress. A sensitivity analysis identifies the key geometric design variables, and response surface methodology is applied to find an optimal shape that maximizes the reaction force at yielding. The proposed simulation-driven workflow offers practical design guidance for enhancing the stability of cable carriers during non-ideal overshoot events.