Non-stability factors affect stability of radial ring rolling process, and lead to fluctuating of ring position. This decreases rolling precision. Evaluating stability of the process is very important. A stability evaluating method is proposed. The stability can be measured with the mean square root of sequence of oscillation of ring geometrical centerline displacement. Using ABAQUS/Explicit, the stability is analyzed. It is showed that guide-roll position angle has the significant effect to the stability. If guide-roll is located at the tangential position to the ring’s fringe, the stability will vary with the angle between two planes. One passes through axes of guide roll and ring blank, and another passes through axes of drive roll and ring blank. The stability is highest when guide roll is situated at the position angle of 100˚to 130˚at exit side of ring rolling mill.