The linear governing equations of a micropolar thermoelastic medium without energy dissipation are solved for surface wave solutions. The appropriate solutions satisfying the radiation conditions are applied to the required boundary conditions at the free surface of the half-space of the medium. A frequency equation is obtained for Rayleigh wave in the medium. The non-dimensional speed of the propagation of Rayleigh wave is computed for a specific model of the material and are shown graphically against frequency and non-dimensional parameter.