Parametric identification of vibrating systems is the process of developing finitely parametrized models for such systems based upon measured excitation and/or response signals. Typically, the excitation is force and the response vibration displacement, velocity, or acceleration. A typical identification experiment is depicted in Figure 1. The structural dynamics are represented by a transfer matrix G…s†, with s indicating the Laplace transform variable. The measurable force excitation vector is fx…t†g, while the measurable vibration response vector (forced if x…t† 6ˆ 0, free if x…t† 0) is fy…t†g and is assumed to be corrupted by stochastic zero-mean noise fn…t†g, which is uncorrelated with fx…t†g (t indicating continuous time). In contrast to nonparametric identification, which leads to nonparametric representations such as frequency or impulse response functions, parametric identification (also called model-based) leads to finitely parametrized models such as difference/differential equation and modal models. Such models provide important benefits due to their: (1) direct relationship with differential equation or physically significant modal representations used in engineering analysis; (2) improved accuracy and frequency resolution; (3) compactness/parsimony of representation, that is, their ability to provide complete system characterization by relatively few parameters; and (4) their suitability for analysis, prediction, fault diagnosis, and control. The price paid for these benefits includes a generally increased identification complexity and dependence of the results on the assumed model form and the estimation criterion. The Elements of Parametric Identification