The basic step in the substructure approach based on discretization of the soil medium for the soil-structure interaction problems is to determine the impedance functions which are defined as the complex dynamic-stiffness coefficients of the soil-footing system are used in the analysis of foundations vibrations. In this study, the discrete values of impedance functions over wide ranges of frequency-factors are presented for both surface-supported and embedded foundations. The numerical results are obtained by using the substructure approach in the frequency domain which is formulated on basis of the Boundary Element Method derived from the fundamental solution for a homogeneous, isotropic and linear-elastic continuum. To further demonstrate in practical applications and to show the solutions of this type of problems to civil engineers, a comprehensive parametric analysis and systematic calculations are performed with various controlling parameters to evaluate the dynamic response of the vibrating soil-foundation system. In addition, the solutions for normalized stiffness and damping coefficients of foundations in almost all cases of vibration modes are in very good agreement with the published results based on the analytical methods. The obtained numerical results should enable practicing engineers to take into account the linear soil-structure interaction problems over wide ranges of frequency factors. (c) 2005 Elsevier Inc. All rights reserved.