Engineered Damping Treatments (EDT) that have high damping characteristics per unit volume are presented. The EDT's under consideration, consist of cellular viscoelastic damping matrices with optimally selected cell configuration, size and distribution. The cellular topology of the EDT's is designed using Computer-Aided-Design (CAD) strategies and the obtained optimal configurations will be manufactured using the state-of-the-art technology of Rapid Prototyping (RP). The EDT's are modeled using the finite element method in an attempt to determine the optimal topologies that maximize the strain energy, maximize the damping characteristics and minimize the total weight. The CAD files of the prototypes of the EDT's. The damping characteristics of the manufactured EDT's are evaluated and compared with the corresponding characteristics obtained by conventional solid damping treatments in order to emphasize the importance of using optimally configured damping treatment to achieve high damping characteristics. The presented procedures are invaluable for designing efficient damping treatments for many military and civilian structures whose vibrations and noise must be effectively controlled.