The present work seeks to optimize the spatial distribution of damping in structures with boundary damping. This work is motivated by design considerations, such as weight and cost, that often limit the amount of damping that can be used. In such cases, the designer must choose the spatial distribution of damping in order to reduce the structural vibration. One intuitively expects that the presence of boundary damping affects the optimal distribution of damping in the structure. In particular, one expects that the optimal design places damping treatments away from such boundaries in order to achieve an even distribution of power flow from the structure. To investigate this effect, finite element models of vibrating structures are developed in which the spatial distribution of damping is parameterized. These parameters are regarded as optimization parameters that are searched to minimize a cost function related to vibration or noise, such as the average response of the structure over a frequency band. Examples are presented that illustrate the effect of boundary damping on the optimal distribution of damping.