Resonators with an equidistant spectrum are required in optics quite often. One of ways to obtain them is to use degeneracy of the frequencies of the resonator modes, which is observed, for example, in well-known confocal resonators. At the same time it is possible to find configuration of the ring resonator with a similar properties - confocal ring resonator. In the first approximation, the ring confocal resonator can be obtained using several (at least three) reflecting surfaces: flat and concave toroidal with the radii of curvature in the two main meridional sections ensuring the fulfillment of the confocality condition and the degeneration of the spectrum. Such resonators can be manufactured as a single monolithic element (prism) and used, in particular, as sensing elements of miniature optical gyroscopes. This work is devoted to the study of the properties of ring confocal resonator with the use of multiphysical modeling.