Wind farms with shared mooring lines have the potential to reduce mooring costs. However, such wind farms may encounter complex system dynamics because adjacent wind turbines are coupled. This paper presents an analysis of the shared mooring system with a focus on the system natural periods. We first apply Irvine’s method to model both the shared line and the two-segment single lines. The response surface method is proposed to replace iterations of the catenary equations of the single lines, and a realistic single line design is presented for OC3 Hywind. Then, system linearization and eigenvalue analysis are performed for the wind farm consisting of two spar floating wind turbines, one shared line, and four single lines. The obtained natural periods and natural modes are verified by numerical free decay tests. Finally, a sensitivity study is carried out to investigate the influence of mooring properties. It is found that the shared line has a significant influence on the natural periods in the surge and sway modes. The natural periods in the surge and sway modes are also most sensitive to the mooring property variations. Two sway eigenmodes are identified, and the lower sway natural period varies between 23 s and 88 s in the sensitivity study. The present analysis method can be used to identify critical natural periods at the preliminary design stage of shared mooring systems.