The wave‐guide mode theory of VLF propagation for a sharply‐bounded homogeneous ionosphere is refined to include stratification at the lower edge of the ionosphere. The numerical results for a two‐layer model are discussed in detail. By choosing the upper medium to have a conductivity with a factor of 10 greater than the lower medium, the attenuationvsfrequency characteristic of the model is consistent with experimental data from 1.0 to 20 kc. The effect of the finite thickness of theElayer, important for frequencies less than 1.0 kc, is treated by an ionospheric model which has a sharp lower edge and an exponential taper to zero at greater he