A powerful dynamic system identification method is proposed for the determination of the characteristic response function of a class of dissipative (e.g., rheological) material-systems from an experimental dynamic system analysis. In this context, a model of rational function of polynomials for the so-called "transfer response function" is assumed. In this context, a discrete-time system analysis method is first introduced to identify the order and parameters of the model. Second, the characteristic function of the system is obtained by using an inverse integral method. The numerical scheme and pertaining examples for testing the model are presented. It is concluded that the proposed procedure, although powerful, is easy to use, and the pertaining model is accurate and efficient. (c) 2005 Elsevier B.V. All rights reserved.