Of the many methods available for achieving effective vibration damping, adding viscoelastic lamina constrained by a stiff elastic materials is an inexpensive, space efficient means for achieving significant damping levels. Recently, the desire to apportion this material in a way that will take the greatest advantage of its dissipative characteristics has led to studies in optimization1-7. The aim of this research is to determine the optimal shape of a constrained viscoelastic layer on an elastic beam used for vibration damping by means of topology optimization and to experimentally verify these results. The optimization objective is to maximize the system loss factor for the first resonance frequency of the base beam. All previous optimal design studies on viscoelastic lamina have been size or shape optimization studies assuming a certain topology for the damping treatment (with the exception of Lumsdaine8 and Lumsdaine and Pai9, of which this work is an extension). In this study, this assumption is relaxed, allowing an optimal topology to emerge. The loss factor is computed using the Modified Modal Strain Energy Method10 in the optimization process. It is observed that a novel topology emerges from the optimized result. From this computational result, a topology is interpreted that can be reasonably manufactured, and this topology is custom fabricated to experimentally validate the computational result. The experimental results show that significant improvement in damping performance, over 300%, is obtained by optimizing the constrained damping layer topology.