In this paper a wave approach, known as the ray tracing method, is used to analyse the vibration performance of a Micro-Electro-Mechanical Systems (MEMS) ring-based rate sensor. This approach uses propagation and transmission of elastic waves, and fully exploits the presence of cyclic symmetry to determine the vibrating response. Sensor sensitivity is highly degraded by the presence of damping. Support loss is one of the important sources of damping in MEMS resonators and takes account of the energy dissipated through the supporting structure. Using classic wave theory in a two-dimensional thin plate, analytical expressions are obtained for substrate displacements due to shear and normal stresses being applied to its edge, and these displacements are used to determine the support loss. Numerical results for the natural frequencies and mode shapes of a MEMS ring-based rate sensor are provided and it is shown that they are in very good agreement with a finite element analysis. The corresponding support losses are also presented.