A numerical time domain approach to radiation and scattering problems is introduced for surfaces of arbitrary conductivity. This approach is based upon a method of moments solution of the electric field integral equation. The problem is posed as a second-kind integral equation in discrete time for those regions of the surface with finite conductivity; it is shown that this formulation possesses desirable stability properties. The numerical method introduced is used to determine the far field radiation of both directive and nondirective transient antennas excited by temporally compact, ultrawideband pulses when the antenna surfaces are subject to a Wu-King surface impedance profile. Such loads are shown to suppress the “late time ringing” resulting from reflected surface currents without significantly affecting the initial radiated waveform. In the case of nondirective transient radiators, such as the bicone or bow tie antenna, the presence of a surface loading has no effect on the peak radiated field strength. In the case of a directive transient radiator, such as a transverse electromagnetic horn, the introduction of a surface impedance reduces the radiated field strength somewhat. The difference in the physical behavior of these two classes of antenna is accounted for.