Small, overlapping platelets of structural material mixed in a matrix of viscoelastic damping material form a dual-phase damping material. This composite is an excellent extensional damping treatment because the viscoelastic damping material can be chosen for environmental resistance and high damping without regard for stiffness. The high extensional stiffness necessary in a good additive damping treatment can be obtained by incorporating the stiff platelets. Analysis of simplified, regularly oriented platelet configurations shows that, when the composite is deformed in extension, the platelets extend and the damping material between them shears. As a result of this type of deformation, the dual-phase material combines some of the better features of constrained and extensional damping treatments. The frequency range of the dual-phase material is broader than that obtained from constrained layer treatments while the damping of the treatment can be designed to be nearly as great as that of the viscoelastic matrix. The analysis presented agrees reasonably well with experimental data and has broad implications for filled materials.