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Abstract: The effect of a metal layer over an elastic substrate on surface acoustic wave propagating in the structure can be evaluated precisely for semi-infinite solids and infinite plates, but there is no accurate analytical solution if the finite size of the plate has to be considered. By expanding displacements with eigensolutions of surface acoustic waves in a semi-inifite solid, a set of two-dimensional equations similar to the Mindlin plate theory are obtained. Then for a thin electrode layer, the effect is considered through the approximation of displacements in the metal layer with the ones in the substrate, and an integration over the thickness incorporated the properties of the metal layer into equations through the modification of material properties with the decaying indices of surface acoustic waves and the thickness of the metal layer. Using AT-cut quartz crystal as the substrate, we present the effect of silver electrode layers of finite thickness on the phase velocity of propagating surface acoustic waves. [Copyright &y& Elsevier]