Viscoelastic materials are extensively used to damp flexural vibrations of metallic structures; it has been known for some time that the energy dissipation due to shear strain in the viscoelastic layer can be increased by constraining it with a stiffer covering layer. In this report, we discuss a method for increasing this damping by cutting the constraining layer into appropriate lengths. The analysis for a single layer of this treatment is relatively straightforward. The damping can be increased still further by using several layers; in this case, the analysis is based upon effective complex elastic moduli of an equivalent homogeneous medium. One result found from this analysis is that, for optimum spacing of cuts, the damping depends primarily upon the stiffness of the constraining layer and only slightly on the shear modulus of the viscoelastic layer. Experimental data are presented for comparison with the theoretical predictions.