In seismic engineering, the soil impedance matrix is a complex function of the frequency. It can be computed using classical numerical methods, but simpler lumped-parameter models are often used. Among these, the most famous are Winklerspring models and those derived from the works of Wolf. A more general model, called the hidden variables model, is presented in this paper. It is based on the study of the mathematical properties of impedance matrices, such as the causality and the stability. The identification method for this type of models is presented in detail. Two applications, of interest in seismic engineering, are described.