When a ship is subjected to an impulsive load, such as when a descending anchor is suddenly deployed, it will execute elastic vibrations in addition to whatever rigid body motions are excited. Of these vibrations some are observed only locally and some are observed throughout the hull. The latter vibrations, also called beam like vibrations, are generally found in beams that are free in space. Although the surrounding water plays an important role in these vibrations, it does not destroy their beam-like characteristic and it is helpful to consider the vibrations of the ideal solid beam to be in free space. A beam free in space may undergo four principal types of elastic deformation designated as bending, twisting, shearing, and extensional deformations. These all can occur simultaneously. Even though the relative magnitudes of bending, shearing, and torsion may be very different with respect to the different axes, these same types of deformation may exist with respect to any of the three principal directions in a solid beam. The purpose of this chapter is to provide detailed information about global and local vibrations, beam theory of ship and steady-state ship vibration, damping of hull vibration, and noise control.