The aim of this paper is to examine the optimal shape of an unconstrained viscoelastic damping material on an elastic beam, and to examine how changing the volume of damping material affects the optimal shape. The optimization objective is to minimize the peak displacement of the beam at the first resonant frequency. The material loss factor is monitored to determine the improvement in performance between an initial, uniform layer shape and the optimized shape. A fine mesh validation model is created to verify the optimized shape. The ABAQUS finite element code is used to model the structures. Elasticity theory based continuum elements are used so that all stress effects are taken into account in the models. The optimization code uses a Sequential Quadratic Programming algorithm. Optimization studies are performed for a range of different damping layer volumes, from layers with 10% to 200% of the volume of the base layer. Results show that significant improvements in performance are obtained in all cases by optimizing the damping layer shape, up to 6000% in some cases. The amount of improvement achieved increases as the damping layer volume increases up to a point. At a certain point, however, (depending on the thickness of the base layer), the amount of improvement between a uniform damping layer and the optimal damping layer may actually decrease significantly.