This thesis examined the potential sound insulation benefit by using damping material to absorb vibrational energy along its transmission path. Statistical Energy Analysis (SEA) was used to evaluate the effect on system performance of adding damping globally, as well as its influence on individual transmission paths. Nine different theoretical models were studied using both bending only and three-wave SEA models to predict the system behaviour in different frequency regions. The results suggest that global damping treatment generally increases the sound insulation in buildings. Initial increases in the internal loss factor (a term used in SEA to describe material damping properties) were found to provide significant initial improvements in sound insulation and flanking paths as opposed to direct paths were found to benefit more from damping treatment. A simple approximation was proposed to predict the damping benefit of paths of specific order without the need to run a full SEA model. In the presence of heavily damped structural element, where SEA is less likely to provide accurate prediction, a forward ray tracing algorithm was proposed as a supplement. It enables one to predict the energy transmission through a heavily damped component coupling two or more lightly damped components (or SEA subsystems). The energy distribution along the edges of the damped component was studied. The contribution from the direct field was found to dominate the incident energy and resulting transmission, especially in areas close to the source when damping is high. Different passive damping treatment techniques were reviewed as well as the theoretical damping level that is achievable as a guidance for theoretical and experimental validation. Several damping measurement techniques were studied and experimental validation of the ray tracing code was undertaken.