Abstract: The circular ring will experience a special kind of deformation under a uniformly distributed torsion and is apt to jump. The stability is an important factor not to be overlooked. In this paper, the equilibrium path is derived for the circular ring of circular cross-section under the uniformly distributed torsion based on the principle of the minimum potential energy. With the energy criterion for the system’s stability, the stability of the equilibrium, the deformation and the moving process of the circular ring are analyzed. Finally, the maximum value of the internal force on the circular ring's cross-section is obtained in the stable equilibrium state.