The propagation of the Rayleigh surface wave in an isotropic elastic material subjected to a homogeneous strain is studied theoretically. The displacement of the wave is assumed infinitesimally small, and its propagation direction is taken to be arbitrary. By the practical approximation that the second and higher orders of the initial strain are neglected, the formula for the change of the propagation velocity due to the strain is derived. In this analysis, the SH component of the wave cannot be assumed small and plays an important role, but it is finally ascertained that the resultant mode of the wave is almost the same as that in the linear theory of elasticity and the SH component contained in the mode is of the first order of the strain.