Abstract
In general the foundation ground is considered as an elastic, isotropic and homogeneous semi-infinite solid. But the soil is deposited in horizontal layers and the elastic properties differ in horizontally and vertically. So we will consider the case of horizontally isotropic and vertically aeolotropic medium. Such a medium is called "transversely isotropic". In the present paper we deal with the propagation of vibrations of a semi-infinite transversely isotropic solid that is subjected to a vertical point exciting force on its surface, now known as the "Dynamic Analogue of Boussinesq's Problem". The problem is axisymmetry and its solutions are obtained by Hankel transformation. By use of these solutions, we will discuss the characteristics of displacements.
