The sealing surfaces subjected to the hydrostatic load from the sealed fluid can deform to such an extent that leakage occurs when the sealed fluid pressure is sufficiently high, and this critical pressure that the seal can sustain without leakage is a fundamental aspect of the seal design. This paper presents a new numerical method based on the bisection algorithm and the boundary element method, which can be utilized to capture the critical pressure with high accuracy. The present method is employed to study the relationship between the critical pressure and the non-planar geometry of the sealing surfaces, under a wide range of loading conditions. The results show that the critical pressure can be acquired from the surface’s dry contact state with a dimensionless correction factor.