The tetrapod jacket-supported offshore wind turbine is subjected to marine environmental loads, resulting in monotonic and cyclic lateral-compression-tension interaction behavior of the pile-soil system. Although the excellent applicability that has been demonstrated by three-dimensional numerical simulation for aiding the revelation of the mechanism of jacket foundation-soil interaction, a significant challenge remains in accurately reflecting the nonlinear stress-strain relationship and cyclic behavior of the soil, and others. Finite element numerical models are therefore established for laterally loaded tetrapod jacket pile foundations in this study, and a bounding surface model is adopted to simulate the elastoplastic characteristics and cyclic ratchet effect of the soil. Subsequently, a parametric analysis is conducted on different net spacings and aspect ratios of the jacket base-piles to investigate the pile deformation characteristics, bearing mechanisms, evolution of pile-soil interaction, and the internal force development under monotonic and cyclic conditions, respectively. The results indicate that under monotonic loading, the pile deformation pattern transitions from a flexible pile mode to a rigid rotational deformation mode as the aspect ratio decreases. Under cyclic loading, attention should be paid to the asynchronous accumulation of axial forces within the base-piles and its impact on overall bearing performance.