A complete solution of thermoelastic dilatational waves in an elastic, heat conducting, homogeneous, and isotropic medium has been obtained for both the steady and unsteady states. Discussions of the solution for a wide range of frequencies and various values of the coefficient of rise (or decay) have been made and the result has been applied to the explanation of the unusual seismic waves recorded from an underground atomic explosion of September 19, 1957, in Nevada. Reflection and retraction of plane waves at plane boundary and plane interface between two media have been studied. The surface waves have also been studied. The solutions of spherical and cylindrical dilatational waves have been found. / Ph. D.