Proposed future space missions involve large structures which must maintain precise dimensional tolerances even during dynamic maneuvers. In order to attenuate disturbances in the many modes of vibration of such a structure, active and passive vibration control are proposed. The passive control is to be achieved by placing viscous or viscoelastic members or materials within a structure in order to absorb energy. Ascertaining the best combination of locations for such treatments is difficult due to the large number of cases, each of which requires computationally expensive complex eigenvalue analyses of a finite element model to compute modal damping values;In this work, a simple model is developed and used to accurately estimate modal damping ratio for any damping case based on a relatively small number of real eigenvalue (normal mode) analyses. The motion of the spring-mass system assumed by this compliant model is modified by placing the damper to be added in series with another stiffness inherent to the structure for each mode and damper location. The compliant models for various modes are then integrated into a unified spherical model. The resulting expression for damping is easily evaluated and optimized. The method is compared to other means of estimating damping such as modal strain energy and reduced vector subspace;Using the spherical compliant model, optimization proceeds much more quickly than would be possible using direct evaluation of modal damping using complex eigenvalue analysis. Once the damping performance criterion is established, the individual candidate locations for damping struts are ranked according to their contribution to similar performance criteria. Locations which span the octahedral cells of the tetrahedron truss of the bulkhead of the example SPICE structure rank highest;To find the optimal locations, combinations of damping strut locations are selected, using the highest ranking strut locations first. Each combination is optimized for damping by golden section using the compliant model. Augmented probabilities based on strut rankings aid a simulated annealing algorithm in selecting each combination to be evaluated.