In media with cubic symmetry, elastic surface waves are only possible on (100) and (110) planes. Previous attempts at describing propagation on these planes have not been altogether successful. In this paper, we make use of the concepts of ‘slowness curve’ and ‘wave curve’ to obtain details of surface waves which can be propagated on (100) and (110) planes. The theory is illustrated by diagrams of the slowness and wave curves of a number of materials, the data for the graphs having been obtained by numerical calculation.