Generally, most of the electronic equipment need a metallic enclosure in order to mechanically protect and electrically shield the interior printed circuit boards (PCBs) and subsystems. But in practical situations, the apertures or slots of various forms are essential parts of the shielding enclosure for thermal dissipation, CD-ROMs, connectors, I/O cabling and so on. The performance of shielding enclosures for high-speed digital systems is compromised by these inevitable discontinuities on enclosure. To minimize the electromagnetic interferences and susceptibility risks by these discontinuities, the shielding enclosures with apertures should be designed based on thorough analysis about the electromagnetic coupling mechanism through apertures. In this paper, the effect of apertures and oblique incident plane wave on shielding effectiveness of the enclosure is studied with the Circuital Approach, and the Finite-Difference Time-Domain method, the simulated SE data are verified by experimental technique. Good agreements are found between these approaches.