In order to identify the dominant flexible modes of a flexible structure with an input/output delay, a numerical method is proposed. The method uses a frequency domain approach (frequency response data) to estimate the resonating frequencies and damping coefficients of the flexible modes, as well as the amount of the time delay. A sequential NLLS (Non-Linear Least Squares) curve fitting procedure is adopted. It is illustrated that such a Newtonian optimization method has the capability of finding the parameters of a reduced order transfer function by minimizing a cost function involving nonlinearities such as exponential and fractional terms.