The transmission of SH waves across a step-like irregularity in the surface of an elastic half-space is considered. A new method has been given to derive an integral equation formulation of the problem. Propagation from the higher to the lower side as well as from the lower to the higher side has been considered. The integral equations, in both cases, have been asymptotically solved for large distances from the step. It is found that for propagation from the higher to lower side there is an increase in the amplitude of the transmitted wave, while there is a decrease in the other case. There is also a change in the phase.