This paper describes lateral propagation of surface acoustic waves (SAWs) when two types of SAWs are coupled. For the analysis, the thin plate model proposed by the authors is extended to include interaction between two SAW modes. Firstly, lateral wave propagation in an infinitely long periodic grating is modelled and discussed, it is found that SAW slowness curves can be changed by mode coupling. Then, the model is applied to the analysis of two-dimensional SAW propagation on the Al grating on the 42°YX-LiTaO3 (42-LT) substrate structure to investigate how the lateral SAW propagation changes with the Al grating thickness. Finally, SAW resonators on 42-LT substrate with Cu electrodes are fabricated and the results confirm the feasibility of the model.