Abstract: Objective This study investigates the prediction of shock response for shipboard equipment subjected to underwater explosion shocks, focusing on theoretical research into the shock response prediction of nonlinear coupled vibration isolation systems and optimization analysis for shock resistance performance.Methods First, to analyze the system response under underwater explosion shock environments, a theoretical shock response prediction model was established, accounting for the stiffness and damping characteristics of nonlinear vibration isolators, limiters, and flexible joints. Subsequently, the Laplace transform and residue theorem were applied to solve the governing equations, obtaining the system's displacement and acceleration responses. The results were compared and validated against finite element numerical simulations and experimental data. On this basis, the key parameters of the system were optimized using the multi-objective genetic algorithm (NSGA-II). Results The results indicate that the shock response of the nonlinear coupled vibration isolation system under underwater explosion shock agrees well with the finite element numerical simulations and experimental results, verifying the reliability of the theoretical model. Conclusion The optimization results demonstrate that different combinations of component stiffness can effectively reduce either the acceleration or the displacement response, playing a regulatory role in the shock resistance performance of the equipment. The findings provide a theoretical foundation and practical guidance for the shock-resistant design and performance optimization of nonlinear coupled vibration isolation systems in underwater explosion shock environments.