Summary: A formulation of a component mode synthesis (CMS) free-interface method is presented and tested on different examples of unforced nonclassically damped systems with symmetric mass, stiffness, and damping matrices. Excellent agreement of the results with the exact ones (unsubdivided systems) is obtained. The selection procedure for component eigenvectors (modes) has been generalized from the undamped system case to the damped one. A new approach (method of weak springs) is developed to treat unconstrained components. The case of periodic force excitation is considered, and a modal analysis technique is developed in which system eigenvectors calculated by the CMS method are used to obtain the forced steady-state response of the system.