Deep-sea aquaculture can alleviate the spatial and environmental pressure of near-shore aquaculture and produce higher quality aquatic products, which is the main development direction of global aquaculture. The coastline of China is relatively flat, with aquaculture operations typically operating in sea areas with water depths of approximately 30–50 m. However, with frequent typhoons and poor sea conditions, the design of mooring system has always been a difficult problem. This paper investigated the multiple cages, considering two layouts of 1 × 4 and 2 × 2, and proposed three different mooring system design schemes. The mooring line tension of the mooring systems under the self-storage condition was compared, and it was observed whether the mooring line accumulation and the contact between the mooring line and the steel structure occurred on the leeward side. Additionally, flexible net models were compared with rigid net models to evaluate the impact of net deformation on cage movement and mooring line tension. Finally, based on the optimal mooring design, the dynamic response of the mooring system under irregular wave conditions was analyzed and studied, providing important reference for the safety and economic design of the mooring system of multiple fish cages.