The magnetostatic analysis is important on corrosion detection problems, nondestructive inspection of structures and biomagnetism measurement. Boundary element method (BEM) is often used to the magnetostatic analysis conventionally because BEM does not require the discretization of the magnetostatic field domain and has an advantage for open domain problems. On the other hand, 2D BEM is more accurate and more efficient than 3D BEM to calculate the electrostatic field of flat plate shaped and thickness uniform electrostatic field domain. However, in case of the magnetostatic field should be calculated, the conventional method requires numerical calculation of electric potentials at discrete sample points in the electrostatic field domain, and numerical region integration of the discrete points. This research has developed a new boundary element method for analyzing magnetostatic field induced by flat plate shaped and thickness uniform electrostatic field domain. This method describes magnetic vector potential and magnetic flux density as the similar form of 2D BEM for the electrostatic field analysis. Since the magnetostatic field can be calculated directly from the results of 2D BEM for the electrostatic field analysis, the accuracy and computational time are improved. In order to demonstrate the accuracy and efficiency of the present method, some example problems are solved and the results are compared with the conventional method. Present method is also applied to the practical problem which is an inspection of lithium-ion batteries.