One of the methods for increasing the service life of stress-cycled structural elements for various purposes is to improve the damping capacity. There are various ways to increase damping, one of which is the use of damping layers. The article investigates the effect of 3M damping tape on the three-layer clamped-free beam dynamic characteristics. The results of natural frequencies experimental studies and logarithmic decrements for free vibrations of an aluminum beam-plate without damping layers (single-layer beam) and with damping layers glued to the front surfaces (three-layer beam) are presented. The dynamic characteristics are calculated based on the amplitude-frequency characteristics analysis obtained by the fast Fourier transform method. The samples’ physical constants are predetermined in static tests. For a given three-layer Euler-Bernoulli beam, its lowest natural frequency is theoretically determined and compared with the frequency calculated on the basis of the Timoshenko model. To determine the three-layer beam decrement with damping layers, a numerical solution of the inverse problem is obtained.