It is nowadays well known that, for certain seismic and soil environments, soil-foundation-structure interaction may play a significant role in the seismic response of structures founded on piles. In such cases, detrimental or beneficial effects should be determined by performing comprehensive soil-structure interaction analyses accounting for both the soil-foundation compliance and the modified seismic input (e.g. filtering effect of the deep foundation). When soil-structure interaction has to be considered, the sub-structure approach may be applied: the frequency dependent soil-foundation dynamic stiffnesses are separately determined and the superstructure is analysed on relevant compliant restraints. This method is valid also in the case of nonlinear behaviour of the superstructure introducing the foundation compliance by means of suitable lumped parameters models with frequency independent parameters.Despite its versatility, the sub-structure approach is demanding because lumped parameter models have to be calibrated after preliminary frequency domain analysis of the soil-foundation system carried out with dedicated software, usually not available to practitioners.In this paper a lumped parameter model is constructed and, with reference to square pile group foundations, simplified formulas are presented for estimating its parameters. The model is able to reproduce the translational, rotational as well as the roto-traslational coupling behaviour of the soil-foundation system. Formulas are calibrated from results of an extensive non-dimensional parametric investigation considering both head-bearing and floating pile groups. These may be readily adopted by engineers to define lumped parameter models that may be implemented in common software for structural analysis.