This paper presents a time domain approach for the analysis of the coupling between an electrostatic discharge (ESD) current and the internal region of a shielded enclosure with a slot. The application of the equivalence principle allows us to obtain an integro-differential equation for the unknown distribution of the aperture electric field. The numerical solution is obtained by an iterative procedure developed by the method of moment (MoM) in time domain. The approach is also applied at the case of a transient incident field of a plane wave impinging on the enclosure. The use of proper impulse responses for space and cavity regions make the model efficient from a computational point of view, without losing in accuracy. Theoretical results are validated by measurements.