Soil structure interaction problems can be addressed through a sub-structure approach in which the structure is modelled using a finite element approximation and the soil is represented through frequency dependent impedance functions. In this idealization the equations of motion of the overall system are frequency dependent and the rigorous evaluation of the response in the time domain must be preceded by a frequency domain analysis. For this reason, the evaluation of the linear dynamic response of a soil-structure interacting system is, nowadays, a formidable task for real structures and particularly in engineering practice. In this paper the role of frequency dependence in the inertial soil-structure interaction is investigated with the aim to propose a simplified alternative parsimonious modelling approach to be conducted directly in the time domain. A case study, represented by a pile-soil-structure interacting system, already considered in the literature, is investigated both in the frequency and the time domain and a simplified procedure for the evaluation of the seismic response of soil-structure interacting systems is proposed.