Our objective is to analyze the frequency and the time-domain responses of a two-dimensional lateral inhomogeneity such as an axial conductor which is buried in a stratified earth. Such inhomogeneities in the earth’s structure give complex transients that cannot be interpreted using just a uniformly layered earth model. To proceed, we determine the fields of a thin axial conductor carrying a filamental current situated in the lower medium of a two-layered earth. This infinitely long axial conductor is characterized by a specific axial impedance. The impedance condition can be used to determine the total field response when the source is a magnetic dipole. Some results are presented that show the waveform at the induced current in a buried axial conductor excited by an impulsive current in a vertical magnetic dipole source located on the earth’s surface. A feature of the waveform is the reversal of the polarity that would not occur in the absence of the buried cable.