Rayleigh Wave Equation are significantly important in describes the speed of the wave propagating on the free surface of an isotropic half-space and it is often used as a model for physical phenomena such as large amplitude vibrations of wind-blown, ice-laden power transmission lines. The equation also appears in solution of Lamb’s problem for an impulsive force. Because of its significance, Lie symmetry reduction were chosen to reduce the equation and hence solve the equation. In this paper, calculation of symmetry of the equation was first present, followed by reduction of the equation and hence analytic solution of the partial differential equation was obtained.