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Some traditional applications of structures and devices with homogeneous materials are being gradually replaced by functionally graded materials (FGM) with spatial variation of properties. The analysis of SAW propagating in FGM structures will be different primarily due to variations of material properties and resulting differential equations with variable coefficients. To provide an effective method and accurate results for the analysis of SAWs in FGM structures, we employed the Frobenius method as the only available method for a detailed analysis of SAW in materials with property variations in a linear pattern. Analytical examples are presented to demonstrate the effectiveness of the method and the effect of FGM on changes of surface displacements in SAW propagation.