The objectives of the studies reported in this dissertation are: (1) to evaluate the dynamic impedance of horizontally inhomogeneous, thin soil layers and of piles embedded in such layers; and (2) to provide improved insight into the response of vertically excited piles bearing on a stratum of arbitrary stiffness. The dissertation consists of two major parts. The first part, reported in Chapters 2 through 5, deals with the analysis of the impedances of inhomogeneous soil layers. Vertical, torsional, and horizontal modes of vibration are investigated. Primary emphasis is placed on assessing the effect of the radial variation of the soil shear modulus. The numerical solutions for layer impedances are obtained for several different radial variations of the shear modulus, and are compared with each other and that applicable to a homogeneous soil. The importance of the inertial effects of the soil zone near the pile and the consequences of discontinuous radial variations of soil modulus are clarified. The layer impedances are then used to evaluate the manner and extent to which the dynamic stiffness and damping capacity of piles may be influenced by the weakening of the soil near the pile-soil interface. The second part of this dissertation, comprised of Chapters 6 and 7, deals with the dynamic impedance of a vertically excited pile which is driven through a uniform layer and bears on a stratum of finite depth and arbitrary stiffness. The solution takes due account of the variation of the soil reactions with depth by expressing them in terms of the characteristic functions of the two-layer medium. Comprehensive parametric studies are made to assess the effects of the various parameters involved and to evaluate the applicability of the solution based on the idealization of the soil medium as a series of thin horizontal layers. Comparisons are also made with previously reported solutions for statically and dynamically loaded piles. The results provide improved insight into the mechanism of soil-pile interaction.