The nonlinear finite element method (FEM) was applied to the analysis of the strain distribution in -shaped seal rings acted by internal pressure or the combined action of internal pressure and axial displacement. The results indicate that the maximum Mises equivalent strain exists at the juncture between the exterior surface of the loop and that of the knuckle when the ring is acted by axial compression displacement and relatively large internal pressure, which is in agreement with the practical work conditions of the rings. According to the plastic limit analysis method, the limit internal pressure should be determined based on the strained condition of the juncture between the exterior surface of the loop and that of the knuckle of the ring by using twifold elastic slope criterion. The formulae for calculating the limit internal pressure of the rings were also derived by regression analysis of the FEM results. These formulae can be used in the limit design and the safety assessment of -shaped rings.