The effect of steep lateral gradients on ELF propagation in the earth-ionosphere waveguide is investigated by full-wave calculations based on two different models of the waveguide. In both models, the ionosphere is replaced by a mathematically equivalent upper wall. In one model, the height of the waveguide is taken to vary in the lateral direction, but the surface impedance of the upper wall is assumed constant. In the other model, the surface impedance is taken to vary laterally, but the height is assumed constant. Magnetic field strengths are calculated along various great circle paths through the transmitter and compared with values obtained from the great circle WKB approximation for the same paths. The results for the two models are not very different from each other, and both are in agreement with the WKB results to within 1 or 2 db at distances of several thousand kilometers. (Author)