Propagation over the earth's surface of electromagnetic transient waveforms radiated by lightning return strokes is examined. Radio propagation theory is applied to the particular case of the return stroke current modeled as a series of connected straight line segments. A known current pulse propagates along the line segments as in the discharge of a precharged transmission line. The effects of an imperfectly conducting ground and an anisotropic ionosphere also are considered by using an idealized waveguide model. Signals above about 10 kHz show significant attenuation due to the imperfectly conducting earth, as have been observed previously. There is qualitative agreement between the model predictions and observed transient data, but lack of detail of the earth model limits the applicability of the results.