<p>This study systematically elucidates the intrinsic mechanisms by which a nonlinear energy sink (NES) suppresses multimodal coupled vibrations in cable structures. First, a spatial model of the cable-NES system and a simplified model considering only the first three in-plane modes were established. Using the Galerkin method, the strongly nonlinear governing equations of the system were derived, and high-precision analytical solutions were obtained via the homotopy analysis method, with their validity verified by Runge–Kutta numerical integration. Comparative analysis of the two models demonstrates that neglecting out-of-plane modes significantly underestimates the system's vibrational energy, while incorporating out-of-plane degrees of freedom is essential for accurately characterizing the targeted energy transfer path. Furthermore, the vibration suppression performance of the NES was quantified using amplitude-frequency response curves, and the effects of the NES damping ratio, nonlinear stiffness, and installation location on the suppression bandwidth were systematically investigated. The findings reveal that out-of-plane modes play a significant role in coupled vibrations; the NES achieves targeted energy transfer by activating nonlinear energy channels, thereby effectively suppressing multimodal coupled vibrations. Parametric analysis shows that optimizing the NES damping characteristics, nonlinear stiffness, and placement can substantially broaden the suppression bandwidth, enabling sustained and broadband vibration attenuation. This research provides theoretical foundations and design references for the nonlinear vibration control design of engineering cable structures.</p>