Shared mooring systems, where adjacent platforms are tethered directly to each other, can reduce anchor quantities and mooring line lengths in a floating array but also introduce new modeling and design challenges. This paper presents and demonstrates a first-order approach to modeling and designing shared mooring systems that simplifies these challenges. We formulate a general, linearized model for the force–displacement response of shared mooring systems, including inter-platform couplings. Using this linearization, we realize significant simplifications to the shared mooring system design problem and propose a corresponding design optimization approach. Finally, we demonstrate the complete approach on a variety of shared-mooring floating wind farm layouts with generic design assumptions and constraints. Some fundamental observations about shared mooring systems can be made from the results. Polygonal array layouts with perpendicular anchor positions appear to maximize shared mooring system efficiency. Also, arrays with greater levels of sharing tend to exhibit larger deviations in offsets between platforms. Overall, the results show how the linearized approach can be applied to efficiently evaluate and systematically optimize preliminary shared mooring system designs.