In this paper, a new method, based on the combination of electromagnetic topology (EMT) and mode matching (MM), is proposed for the analysis of the electromagnetic field coupling phenomena from an external field to an inner electric system. The proposed method can solve the electromagnetic field coupling in a complex system accurately and requires a short computation time and reduced memory. To verify the validity of this method, an aperture backed cavity model was analyzed and the electric field intensity in the cavity and the induced surface current on the wire were computed. The results were compared with FDTD results.