he propagation of Rayleigh waves over the surface of a visco-elastic solid is examined. It is shown that for a Poisson solid (lambda = mu ), the behavior of the waves can be characterized by a dimensionless parameter delta = omega eta /mu which is less than 0.1 for the frequencies and elastic parameters of interest in geophysics. In this expression omega = angular frequency, mu = shear modulus, eta = viscosity. For small values of delta it is possible to modify the usual analysis of Rayleigh waves and obtain the new characteristics without much difficulty. It is shown that the motion of a particle on the earth's surface is changed from an ellipse to a Lissajous' figure and that the phase angle between the vertical and horizontal displacements is changed from pi /2 to (pi /2) - 0.1488delta radians. The surface wave has an attenuation factor of 2.908delta /lambda 0 where lambda 0 is the wave length of the Rayleigh wave in the absence of internal friction.