The theoretical principles of anelastic phenomena in solids were formulated for the first time by C. Zener in 1937 – 1938. Virtually at the same time N. N. Davidenkov formulated the principles of the nonlinear mechanics of materials. Special literature operates with various terms for describing inelastic phenomena in solids, for example, internal friction, physical acoustics, absorption of ultrasound, static and dynamic hysteresis loops, internal dissipation of energy, and damping of oscillations. In 1990 De Batist and Magalas suggested a generalized concept for the description of these phenomena known today as mechanical spectroscopy of materials. Mechanical spectroscopy (MS) studies absorption spectra of mechanical energy under the conditions of applied periodic external mechanical field. Mechanical spectroscopy is a powerful tool for the study of materials. In particular, it is shown that such a technique can help the mechanical characterisation of materials.