We consider a problem of waves propagation in a multi-layered piezoelectric substrate under a periodic electrode grating utilizing a full-FEM approach for a unit cell with periodic boundary conditions. The perfectly matched layer is employed in order to truncate the computational domain. The simulations are done for the structures containing one-and two-layered piezoelectric substrates. The COM parameters obtained by the proposed model are compared with those extracted using a FEM/BEM technique.