  Surface acoustic waves (SAWs) are elastic waves localized on a surface of an
elastic body. We theoretically study topological edge modes of SAWs for a
corrugated surface. We introduce a corrugation forming a triangular lattice on
the surface of an elastic body. We treat the corrugation as a perturbation, and
construct eigenmodes on a corrugated surface by superposing those for the flat
surface at wavevectors which are mutually different by reciprocal lattice
vectors. We thereby show emergence of Dirac cones at the $K$ and $K'$ points
analytically. Moreover, by breaking the time-reversal symmetry, we show that
the Dirac cones open a gap, and that the Chern number for the lowest band has a
nonzero value. It means existence of topological chiral edge modes of SAWs in
the gap.
