The penetration of the electromagnetic field through an infinite slot in a conducting plane backed by a conducting-wall channel is examined. The total transverse-electric-to-slot-axis field in the interior of the channel and above the conducting plane is determined by two independent integral equation methods: (1) a coupled integral equation method which can be used to determine the field in the case of a channel with an arbitrarily shaped cross section and (2) a single integral equation method which involves a Green's function specific to the shape of the backing channel. Data from the two methods are presented for the equivalent currents obtained from the integral equations, for the field near the channel-backed slot, and for the actual currents present on the conducting surfaces.