The sealing performance of end fittings is very important for offshore oil and gas pipelines. To investigate the sealing behavior of a ring-shaped wedge seal, global and local numerical models of the ring–pipe interaction have been developed based on the finite-element method. First, the sealing process of the ring under pressure is simulated. Second, a criterion for the penetration of fluid pressure is applied in these models to assess how the sealing capacity changes along the contact surface. Finally, the contact magnitude of interference and the shape of the sawtooth heaves on the sealing ring are predicted and compared. The results show an interesting concentration of von Mises stress in the sealing ring and also that the peak contact pressure appears in the sealing zone. However, the penetration of fluid pressure has obvious effects on the distributions of von Mises stress and contact pressure. The best sealing performance is when the axial displacement of the sealing ring is 1.4 mm and the contact magnitude of interference is 0.3 mm. Given the sawtooth heave of sealing ring, semicircular heave gives the better sealing capacity compared with trapezoidal heave.