Theoretical damping values have been determined for three‐ and five‐layer beams having representative cross sections. Trends are obtained that show damping effects produced by changes in cross‐sectional geometry of the beam and properties of the damping material. The results are a series of characteristic curves displaying an increase in damping with increased frequency for the low frequency range, a peaking of the curves in the midfrequency range and a decrease in damping for the high frequencies. In addition, they show that increased viscoelastic material thickness and increased shear storage modulus shift the damping curve toward the low frequencies, while an increased thickness of the elastic layers, considered herein, appear to have no appreciable effect on composite damping behavior. For equal over‐all beam thickness and equal viscoelastic‐material thicknesses, the three‐layer beam provided higher damping at the low frequencies whereas the five‐layer beam yielded better damping at the peak, and at higher frequencies. Approximate analytical expressions are derived that verify the low‐ and high‐frequency characteristics and predict the peak damping frequency and composite loss factor.