This paper presents a new boundary element formulation for modelling the fundamental symmetric Lamb wave (S0 mode) propagating in the high frequency range. At such high frequencies, the S0 mode reveals significant dispersive character. Conventional BEM formulations governed by the generalised plane stress theory fail to accurately represent the dispersive properties of the S0 mode and to handle out-of-plane loads because the effects of thickness-stretch are not considered. Therefore, a new BEM formulation is proposed based on the dynamic fundamental solutions which are derived for the first time for a higher-order plate theory (Kane–Mindlin) taking into account coupling between extensional motion and the first mode of thickness vibration. Only plate edges are required to be discretized using simple line elements in the proposed BEM formulation. Three benchmark examples are presented where the solutions from the new BEM formulation are shown to be in excellent agreement with analytical and three-dimensional finite element results. Furthermore, the advantage of the proposed formulation is demonstrated through comparisons with the BEM results based on the generalised plane stress theory.