Abstract: Rayleigh surface wave propagation for multiplayer anisotropic materials is studied. Both displacements and stresses are combined into a mixed state vector, from the system of Lagrange to that of Hamilton and so that the orders of differential equations are reduced from two to one. The eigenvalues of wave equations are solved by the precise integration and extended Wittrick-Williams algorithm. The numerical examples have proved the efficiency and precision of this method in anisotropic and isotropic materials.