An analytical formulation has been developed to evaluate the shielding effectiveness (SE) of two coplanar rectangular metallic enclosures with a circular aperture excited by an internal electric dipole source. The formulation consists of three parts: First, the near-field electromagnetic interference (EMI) of the electromagnetic leakage from the aperture is represented by the electric dipole in one enclosure. Then, the aperture equivalent magnetic and electric dipole moments are calculated according to the Bethe's small aperture coupling theory. Finally, the electric field of the other enclosure is derived by using the equivalent magnetic dipole field, equivalent electric dipole field and the corresponding enclosure's Green's functions in the two fields. In this formulation, the electric field of the enclosure can be expressed as a function of the observation point, the aperture's center point, source point, shape of the aperture and enclosure's conductivity. The formulation then is employed to analyze the effect of the above factors on the SE. The analytical results have been successfully compared with the full-wave simulation software Computer Simulation Technology (CST) from 0.3 ∼ 2. 4G Hz.