The physics of electromagnetic wave transmission through narrow slots and lapped joints in thick conducting screens is examined in detail by applying numerical models to compute both field distributions within the slots and joints, and fields transmitted to the shadow region. The primary modeling tool is the finite-difference time-domain (FD-TD) method, using a Faraday's law contour integral approach to develop new and simple modifications of the basic FD-TD algorithm to properly model the slot physics, even when the slot gap width is much less than one space lattice cell. Finely sampled method of moments (MM) models are used to validate the FD-TD tool for relatively simple straight slots; FD-T D is then used to explore properties of more complicated lapped joints which are widely used for shielding purposes at junctions of metal surfaces. It is found that previously reported slot resonances (screen thicknesses at which exceptionally large transmission of energy may occur) occur in a more general sense for lapped joints as path-length resonances. That is, the total path length along the lapped joint from the front of the screen to the back can become resonant, despite the presence of a number of right-angle turns in the joint path. In addition to greatly enhanced power transmission, path-length resonances can result in total fields within the joint exceeding the incident fields by more than one order of magnitude. Sample field distributions for this case are given. This field enhancement might cause sparking and other nonlinear effects during high-power microwave (HPM) illumination, and must be accounted in HPM coupling studies.