While several writings purport to give the history of elasticity and vibration, they are so inaccurate or fragmentary as to imply a general picture of the beginnings of these subjects that is outright false. A new history to 1788, drawn from detailed study of all the available sources, is to be published [C. Truesdell, The Rational Mechanics of Flexible or Elastic Bodies, 1638–1788, Leonhardi Euleri Opera Omnia (Ser. II, Vol. 11, Part 2, to appear in 1960)]. The present article provides a list of some of the specific discoveries described therein. The following pages may not conform to the reader's preconception of the subject, or to his idea of what the history of science ought to be. By a one‐sided selection of material, or by concentration on a particular problem such as that of the vibrating string, it would easily be possible to write a more inspiring tale of continued progress, or a case study in the development of science. Such a tale, such a study, even if correct in facts would serve only to reinforce all too widely received false pictures not only of how science developed but also of what science is. The problems whose history is outlined here were studied in interrelation to one another, not without steps sideways or even backward, and knowledge concerning them was not gotten in what now seems a logical order of development. This outline is intended for a reader already familiar with the modern theories of elasticity and vibration and already interested in their historical origin; its purpose is to answer for such a person questions of a kind most frequently directed to me, namely, “Who first discovered A?” and “What did B do for acoustics?” It is not, it cannot be a history of the subject. History cannot be understood from precis or digests, however accurate. The reader who desires consecutive explanations, equations, figures, and references may find them in my book. If I were to draw any summary moral from this development, it would be that mathematics was a more powerful tool than experiment in founding the classical theories of elasticity and vibration.