A methodology for vulnerable area of voltage sag based on numerical analysis theory is proposed. This method introduces a variety of numerical analysis methods to solve the critical fault points on the basis of the analysis of the sag amplitude. The problem of critical fault point is reduced to the problem of solving the root of the quadratic function, and different numerical analysis methods are used to achieve faster convergence speed under the premise of satisfying the computational accuracy. The method has a wide adaptability to a power system with a given network parameter. The comparison between the results of the fault point method and the single numerical solution and the performance of the algorithm verifies the accuracy and effectiveness of the proposed method for solving the sagging area.