The problem of shielding sensitive measurement equipment, computers and control devices, against the influence of disturbing electromagnetic fields is by no means new. Usually, the metallic shields are used to protect equipment, the sensitive electronic parts of which can be disturbed or even destroyed by transient EM fields. Practical shielding enclosures always contain many apertures such as vents, cable feed-through and seams, which allow electromagnetic energy to couple into the structure. This paper presents a numerical study of the coupling of transient fields radiated during electrostatic discharge (ESD) into the metallic enclosure with an aperture. Computer simulation of the ESD is done using an electrodynamic method based on the method of moments (MoM) in the time domain for discharging bodies of revolution, located near the grounded plane. For a discharging structure like a spheroid the calculated currents and fields are compared with experimental data and are shown to be accurate for EMC applications. Such realistic fields are used in this paper as incident fields to investigate aperture penetration into cavities. The time domain analysis is done using the FDTD method.