Damping is the energy dissipation properties of a material or system under cyclic stress. The vibrational and damping characteristics of composites are important in many applications, including ground-based and airborne vehicles, space structures, and sporting goods. This article describes the damping characteristics of unidirectional composites, when they are subjected to longitudinal shear, longitudinal tension/compression, and transverse tension/compression. It presents equations that govern the overall damping capacity of beams that are cut from laminated plates. The article discusses the effect of temperature on damping and provides information on the relationship between damping and strength.