Continuous and spherical harmonic waves are generated at an internal point of the medium. By use of the classical method of Sommerfeld, the different modes of propagation near a free surface after the arrival of the waves are examined. From the approximate evaluations of the integrals, it is found that in addition to the ordinary types of body and surface waves, there are also inhomogeneous waves and surface waves which are not of the Rayleigh type. The amplitude factors of these latter waves vary inversely as the square instead of as the square root of the epicentral distance. Altogether, there are not less than five different types of waves and they are obtained from integrations in the neighborhood of the singularities of the integrals.