The main objective of this dissertation is to develop a new experimental damping matrix identification method. Newly developed damping matrix identification method consists of finite element (FE) model updating and experimental modal analysis. In order to accomplish the goal of this study, first, the experimental modal analysis which is available for non-proportional viscous damping system is examined. Second, the sensitivity-based FE model updating method using natural frequencies and zero frequencies as target parameters is proposed. Proposed FE model updating method is validated via two examples using numerical and experimental models. Next, an efficient technique, that can identify the structural damping matrix of the damped structure through combination of the experimental modal analysis and the FE model updating method, is developed. The developed method is verified by estimating the damping matrix of a real cantilever beam attached damping material on one side.