The problem of determining linear time-invariant models of flexible structures is considered. The approach is first to identify the modal parameters by using free response measurement records that could be contaminated with noise. The stiffness and damping matrices are then extracted from the identified modal parameters. The identification technique, which is developed in the time-domain is based on least square linear regression theory and is organized as a systematic and easy to implement scheme. The estimates are produced without the need of solving an eigenvalue problem or singular value decomposition of a data matrix. The effect of measurement noise on estimation accuracy is discussed. A numerical example is presented to illustrate the results.