Calculations for the phase velocity of acoustic surface waves on lithium niobate with a contiguous gold layer have been carried out for the fundamental and higher‐order modes of propagation. The anisotropy of the substrate leads to a prediction that the first higher‐order mode has a low‐frequency cutoff. In some cases the phase velocity dispersion curves for various modes have crossing points. Theoretical calculations and experimental evidence of the position of the crossing points for the first two modes and the phase velocity characteristics of the dominant mode above and below the crossing points as a function of the frequency‐film thickness product are given.