An analytical formulation has been developed for the electromagnetic leakage from an apertured rectangular cavity excited internally by an electric dipole. The leakage fields are represented by the equivalent electric and magnetic dipoles located at the aperture center with their dipole moments related to the “closed cavity” field within the framework of the Bethe's small aperture coupling theory. The “closed cavity” field is obtained by using the mode-expansion method. In this formulation, the leakage field can be expressed as a function of the frequency, the source point, the field point, and the position of the aperture. The formulation then is employed to analyze the influences of the above factors on the shielding effectiveness and the corresponding physical mechanisms are also illuminated. Comparison with the full wave simulation software CST has verified the formulation over a very broad frequency range. It is shown that the near-field shielding effectiveness is smaller than the far-field one, and the electric shielding effectiveness is different from the magnetic one in the near-field zone.