Proper mathematical models of structures are beneficial for designers and analysts. The accuracy of the results is essential. Therefore, verification and/or correction of the models is vital. This can be done by utilizing experimental results or other analytical solutions. There are different methods of generating the accurate mathematical models. These methods range from completely analytically derived models, completely experimentally derived models, to a combination of the two. These model generation procedures are called System Identification. Today a popular method is to create an analytical model as accurately as possible and then improve this model using experimental results. This thesis provides a review of System Identification methods as applied to vibrating structures. One simple method and three more complex methods, chosen from current engineering literature, are implemented on the computer. These methods offer the capability to correct a discrete (for example, finite element based) model through the use of experimental measurements. The validity of the methods is checked on a two degree of freedom problem, an eight degree of freedom example frequently used in the literature, and with experimentally derived vibration results of a free-free beam. / Master of Science