Radial ring rolling is an unsteady plastic deformation process. Internal stress of the ring is foundation of formation of the plastic hinge. The radial wall thickness of ring changes gradually along ring circumferential direction. Theoretical analysis and FE simulation show that: the plastic hinge is not always exactly opposite to the rolling deformation zone in ring rolling process without guide-roll. The plastic hinge position angle β0 is affected by ratio of rolling entrance wall thickness H0 and rate of wall thickness change η. Curve of β0-H0/η is shaped as double U staggered relative to each other. With the H0/η increasing, β0 reduces gradually and approaches to π in the range of H0/η>6.28. H0/η>14.6H0/R2. Only when the rolling process is steady, and H0≈R2, β0 is greater than π, and approximates to π. The β0 fluctuates dramatically when H0/η≈5.71. In some cases, H0/η may fluctuate in 0 to 6.28, leading to the instability of plastic hinge position.