A diffraction integral equation for unstable ring resonators with 90° beam rotation is derived using matrix method. A formulation of the equivalent Frensel number for the resonator is obtained. Methods for suppressing the reverse mode are analyzed, and the radius of curvature of the reverse wave suppressor mirror is gaven. Relationship between eigenvalues of the resonator modes and variant magnification factor M is demonstrated by numerical calculations. Mode-fields idstribution curves of a resonator are presented with the magnificationf actor M as 1.2.