The magnetic flux leakage detection is a common nondestructive detection method for ferromagnetic materials with high speed, high sensitivity and simple operation. The finite element model is widely used in magnetic flux leakage detection. The solution accuracy of the finite element model is high. But, the calculation time is long. Therefore, this article proposes a finite element modeling and solution method for fast calculation of 2D defect magnetic leakage field, which can reduce the calculation time while ensuring the accuracy. Through the theoretical derivation of finite element numerical calculation, the finite element model of magnetic leakage field is established. First, the six-node triangular element is used to divide the grid. Then, the sparse matrix is used to solve the equations, and the orthogonal basis of the zero space of the boundary condition matrix is used to solve the magnetic potential. The comparison with the calculation results of COMSOL simulation software shows that the formulated model is correct and feasible. Through the verification of actual testing data, this model has significantly improved performance compared with the traditional finite element model. The maximum accuracy is increased by 83. 49% , and the calculation time can be reduced by 95. 43% . A fast and effective forward model is provided for studying the magnetic flux leakage reconstruction of irregular defects.