Several findings on the modes of a nonplanar ring resonator have been carried out by utilizing the matrix method of generalized Gaussian beams. The widely used nonplanar ring resonator—a four-equal-sided nonplanar ring cavity with two curvature mirrors and two planar mirrors—has been chosen as an example. The overall stability maps of this typical nonplanar ring cavity with L∕R ranging from 0 to ∞ are calculated and described, while the total cavity length is L and the radius of the curvature mirrors is R. The stability map has also been found to have asymmetry with total image rotation ρ ranging from 0° to 360° and 0<L/R<2 . It has also been found that there still exist several stable regions in the extended region with L/R>2 . The Gaussian modes of the nonplanar ring cavity have been found to have different characteristics with different design parameters such as ρ and L/R . The azimuth angles of the major and minor axes of the spot size have been found to be variable with different design parameters such as ρ and L/R and variable under different location of the nonplanar cavity. These interesting findings are totally different from the behavior of conventional planar stable resonators and are important to the cavity designs of nonplanar ring resonators.