The thesis consists of two parts. The first part deals with the historical development of the science of seismology and the application of the mathematical theory of elasticity to that subject. In the beginning m brief sketch of the method of determining the velocity of body waves at various depths inside the earth is given and the major discontinuities described. Features of seismic records are described together with their modification with the increase in epicentral distance. The general theories of the propagation of body waves in isotropic media and the two surface waves due to Rayleigh and Love are discussed with special reference to the heterogeneity of the earth and the phenomenon of dispersion. The second part deals with the generation of surface waves first with reference to the depth of focus of earthquakes and later on the possibilities of their generation under certain circumstances of the reflection and refraction of body waves has been dealt with at some length. In one case it has been found that at a free surface a plane wave of SV type, travelling parallel to the surface, la capable of generating surface waves which are identical with the Rayleigh waves under a certain state of attenuation.