The shielding effectiveness of an apertured rectangular cavity against the near-field waves of both electric and magnetic dipoles is investigated theoretically by using an extended equivalent circuit method. Both electric and magnetic shielding effectivenesses are calculated as functions of distance between the dipoles and the enclosure. It is shown that the near-field shielding effectiveness is lower than the far-field (plane-wave) shielding effectiveness. Also, in the near-field region, the shielding effectiveness will reduce obviously with the decrease of the source-to-enclosure distance. Based on Bethe's small aperture coupling theory, analytical formulas are presented to describe the quantitative relation between the near-field and the far-field shielding effectivenesses. It is shown that the results from equivalent circuit method are in good agreement with the relation obtained from the Bethe's theory.