Often resonators with an equidistant spectrum are required in optics. One of ways of their receiving is the degeneracy of the frequencies of the resonator modes. For example, it is observed in the well-known classical confocal (linear) resonator. At the same time exist similar to him on properties of the configuration of the ring resonators - the confocal ring resonators. In the first approximation they can be received using in the resonator at least one concave toroidal reflective surface with the values of the radiuses of curvature in the two main meridional sections providing performance of the confocal condition and degeneration of the spectrum. For example, such resonators can be used as sensitive elements of miniature optical gyroscopes. For today properties of the confocal ring resonators have not been practically studied. This work is devoted to investigation of the confocal ring resonators with the use of computer modeling.