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A detailed analysis of the effects of finite-thickness apertures on the shielding properties of a rectangular metallic box is carried out through an efficient full-wave code based on the method of moments in the spatial domain. An incident plane wave having arbitrary polarization and incidence angle is assumed as a field source. The evaluation of the cavity Green function is accelerated by an application of the Ewald sum technique with a novel Ewald splitting parameter valid for high frequencies, and a recently proposed integral-equation-based approximate model of the aperture thickness is also applied. Numerical results are validated by comparisons with those obtained by means of commercial codes based on different numerical approaches and show rigorously that the effects of a finite thickness can usually be neglected (at least, at sufficiently low frequencies), with the noticeable exception of long slots. The effects of common limiting assumptions adopted in the study of enclosures with zero-thickness apertures are also investigated.