The paper proposes a new methodology for the control of residual displacements in multi-storey steel structure frames. The work starts from the validation and extension of a mechanical model based on single degree of freedom systems, already proposed in previous work, following with analyses performed on a set of natural accelerograms. The same model is applied to multi-degree of freedom (MDOF) systems through an anlaytical design procedure. The procedure is used to dimension study cases composed of concentrically braced frames that are analysed through nonlinear dynamic analyses with earthquake records excerpted from the previous dataset. The results confirm the effectiveness and suitability of the proposed procedure for MDOF systems. ……