Abstract: Tensegrity ring structures are predominantly employed as antenna structures in the space sector. However, their form-finding problem is inherently challenging and relatively under-researched. To streamline the analysis process and enhance the versatility of the method for different topologies, a novel approach to form-finding for tensegrity rings is proposed in this study. The proposed method involves the division of the coordinate and force density vectors into transformation matrices multiplied by the eigen parameters, the acquisition of these eigen parameters through SVD (singular value decomposition), and the repetition of the two eigen parameters to facilitate the structure's convergence to a stable position. The method is particularly well-suited to toroidal structures, which possess the property of having the centre of symmetry coincident with the centre of a circle. The feasibility and high computational efficiency of the method are validated by numerical examples, which demonstrate that it significantly reduces the difficulty of form-finding for regular ring tensegrity structures and remains efficient under different initial conditions and numbers of modules. Furthermore, the method avoids complex parametric modelling analysis and simplifies the complexity of form-finding. It is anticipated that the method will be extended in the future to the form-finding analysis of other regularly distributed structures.