An efficient analytical method based on the Cohn model and mirror procedure is proposed for the prediction of the shielding effectiveness (SE) of a rectangular enclosure with electrically large apertures. Firstly, the coupled electromagnetic fields are represented by the equivalent dipole moments located at the centre of the aperture according to the Cohn model, where the dipole moments can be calculated based on the mirror procedure. Then, the vector potentials can be obtained through the relation between the dipole moments and the current distribution. Finally, the total electric fields are obtained by using the vector potentials, thus the SE and most of the resonant modes can be predicted accurately and fast. The SE results which have been verified by the CST over a wide frequency band of 0.01–3.0 GHz show that the proposed method is effective in handling the enclosure with electrically large apertures, including the multiple apertures arranged in different ways and hybrid apertures in different shapes and dimensions.