For a number of years it has been known that flexural vibrations in a plate can be damped by the application of a layer of damping (viscoelastic) material that is in turn constrained by a backing layer or foil. A common example is the damping tape currently used in aircraft.This paper presents a quantitative analysis of the damping effectiveness of such a constrained layer. As in the work of H. Oberst the damping is characterized by the loss factor η, which is the normalized imaginary part of the complex bending stiffness of the damped plate.The calculated damping factor depends on the wavelength of bending waves in the damped plate, and on the thicknesses and elastic moduli of the plate, the damping layer, and the constraining layer. A complex shear modulus is assigned to the damping layer, where all of the energy dissipation is assumed to take place.Damping factors have been determined experimentally on laboratory test bars for a number of constrained‐damping‐layer applications for frequencies from about 100 to 4000 cps over a range of temperatures. Gratifying agreement with calculated damping has been found for variations in frequency, temperature, and damped‐bar geometry.