In a homogeneous plate, Rayleigh waves will have a symmetric and anti-symmetric mode regarding to the mid-plane with different phase velocities. If plate properties vary along the thickness, or the plate is of functionally graded material (FGM), the symmetry of modes and frequency behavior will be modified, thus producing different features for engineering applications such as amplifying or reducing the velocity and deformation. This kind of effect can also be easily realized by utilizing a layered structure with desired material properties that can produce these effects in terms of velocity and displacements, since Rayleigh waves in a solid with general material property grading schemes are difficult to analyze with known methods. Solutions from layered structures with exponential and polynomial property grading schemes are obtained from the layered model and comparisons with known analytical results are made to validate the method and examine possible applications of such structures in engineering.Rayleigh wave, surface acoustic wave, vibration, plate, layered structure, functionally graded material (FGM) Surface acoustic waves (SAW), also known as Rayleigh waves, exist in a semi-infinite solid with a free plane surface. Since its discovery by Rayleigh in 1885 [1] , surface acoustic waves have found wide engineering applications including piezoelectric surface acoustic wave resonators [2] . More general applications in foundations for vibration control and isolation caused by moving loads are also important because surface waves have been the destructive wave component due to its lower velocity (frequency) and energy concentration [3][4][5][6] . Although these applications are drastically different by nature, the common feature we can summarize is that both surface wave velocity and displacements are the major concerns for given structures. For SAW devices, which are widely