Abstract: A theoretical method is presented in this paper,which analyzes properties of surface acoustic waves propagating on metallic gratings with finite thickness and combines a finite element method and a variational principle on surface acoustic waves propagating on periodic metal gratings.Based on D.P.Chen and Haus theory,a finite element method is used to investigate the effects of matallic gratings upon the propagation of surface acoustic waves.The coupling-of-modes parameters contributed by mechanical loading are expressed by the matrix derived from the finite element method.Consequently Chen and Haus theory can also be applied to analyze the properties of surface acoustic waves propagating on metallic gratings with finite thickness and arbitrary shape.Finally,the characteristics of surface acoustic waves propagating under gold and aluminium or silver gratings on a few piezoelectric crystals are studied. Numerical results of the coupling-of-modes parameters of the surface acoustic waves are obtained.