It is significant to analyze the waves induced by buried sources from the point view of the geoengineering prospecting. Based on the mode superposition method, displacement expressions were presented for waves in the homogeneous half space induced by buried spherical and dilatational point sources. Then the excitability and propagation behavior of Rayleigh waves were investigated, and the mechanism of the excitability was also analyzed. In addition, the reliability of the proposed method was verified by numerical simulations. It is shown that the excitability of Rayleigh waves was related to the ratio of buried depth to the wavelength. It is found that the lower the ratio was, the higher the excitability was. However, Rayleigh wave was not easily activated when the ratio was greater than 1. Compared with the normal Rayleigh waves which propagate in the planar wavefronts in the free state, the phase velocity of Rayleigh waves activated by buried sources varied with the propagation distance. Particularly, the activated Rayleigh waves had the spatial behavior. The nearer the distance from the axis was, the lower the phase velocity of the vertical vibration was. When the distance was beyond one wavelength, the phase velocity of the activated Rayleigh waves approached that of the normal Rayleigh waves.