This paper begins with a discussion of various mathematical models which have been proposed to represent the damping behavior of solid materials, with emphasis on their usefulness in structural dynamic analyses. Next the various measures of damping which have been proposed for homogeneous materials are presented, along with derivations of interrelationships which exist among them. A wide variety of experimental techniques have been used to determine the damping characteristics; these are outlined in the next section. The paper concludes with a detailed discussion of excitation and data-reduction techniques for modal response of complicated structures. In an appendix (Appendix I) are presented two new extensions of the Kennedy-Pancu technique to structures made of materials represented by more realistic mathematical models than heretofore used.