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 wave vectors 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. This indicates the existence of topological chiral edge modes of SAWs in the gap.