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Combining with the self-consistent condition and extended 5 × 5 matrix, we theoretically analyzed the polarization properties of the eigenmodes throughout the nonplanar ring resonators with different structures. According to the satisfactory cross section size of the eigenmodes, a comparative study of the stability properties of these nonplanar ring resonators is also provided, and the three dimensions stability space of these resonators are presented for the first time as far as our knowledge goes. The results show that the major and minor axes of the cross section change with the propagation distance and have a symmetrical point for resonators with two different structures, and the area of the stable region for these resonators can be extended by changing the incident angles of the laser beam or the radii of mirror surfaces in the resonator. These interesting results are important for designing and arranging the diaphragm in ring resonators with a nonplanar structure, as well as optimizing the structure of the resonators themselves.