A mathematic model for calculating the ellipticity of the output beams in square planar ring resonators is given. By analyzing the mathematic model, the stress effect of the output mirror has the unsymmetrical influence on the clockwise and counterclockwise ellipticities of output beams. Moreover, the validity of the theoretical analysis is verified by the experiment. Based on these novel results, the method for aligning the light path, which is aligned by measuring the clockwise and counterclockwise ellipticities of output beams, cannot control the distortion angle of square ring resonators effectively.