We develop a theory describing the propagation of a pulse of electromagnetic energy through a gas in which breakdown is occurring (by means of the pulse‐induced electron cascade). The theory is based on solutions to a model wave equation for the pulse electric field, which incorporates the electron cascade in an approximate fashion, and which is derived from the appropriate Maxwell equations coupling the pulse fields to the cascading electron current. Nonlinear effects are ignored, but solutions to the model wave equation appear useful in identifying major trends in the pulse propagation, such as the pulse attenuation and its dependence on the input pulse nominal frequency, spectral breadth, width, rise time, and overall shape. Our results are of relatively simple analytical form, they semiquantitatively confirm available data, and they imply that the pulse energy transport through the electron cascade can be enhanced by choice of certain combinations of the input pulse parameters.