This paper discusses the application of the finite element method to the simulation of surface acoustic wave generation on piezoelectric substrates and the possibility of reducing the number of computations by taking into account the symmetry of the problem. It is shown that the computations can be performed in only one half of the structure provided that the substrate assumes particular orientations. The class of allowed orientations encompasses the majority of crystal cuts used in practice. A test computation of the electric admittance agrees well with experimental results. The perfectly matched layer method is implemented to truncate the computational domain.