Book excerpt: Due to strong potential applications and more demanding requirements imposed upon long and thick cylindrical structures, there has been increasing research and development activities during recent years in the field of vibration and passive vibration control of these types of structures. An important step in the study of cylindrical structures is the determination of their vibration modal characteristics. This modal information plays a key role in the design and vibration suppression of these structures when subjected to dynamic excitations. Most reported studies on the dynamic response of cylindrical structures have been restricted to the application of the shell theories. These theories are based on a number of simplifying assumptions. The most important of which is, the considered shell must be relatively thin to assume constant stresses within the cylinder. Therefore, due to this limitation, shell theories are inadequate to accurately describe all possible vibration modes in thick cylindrical structures. The primary scope of this book is to address these problems by applying the theory of elasto-dynamics.