AbstractThis paper analyzes the influence of horizontal damped and undamped restraints in terms of the amplification of the response of rocking masonry walls subjected to seismic excitations. It also makes a practical contribution to the design of antiseismic devices conceived to control rocking motion, avoiding or at least limiting undesirable response amplifications that would lead to local or global failure. A horizontal restraint, simulating an elastoplastic steel tie-rod, was coupled with a damper, whose action is included in a proposed equation of motion. Parametric analyses were performed for three typical façades of masonry buildings, showing that, if the stiffness of tie-rod increases, the seismic vulnerability of a rocking façade is not necessarily reduced. Therefore, the calculation of rocking spectra is recommended in order to identify stiffness ranges in which amplification could occur. A simple method for calculating the design damping coefficient of a shock absorber is proposed and the consequent mitigation of vulnerability is demonstrated in various analysis configurations. Graphs plotting time-dependent ratios between the energy dissipated by the shock absorber and the seismic input energy are shown to be a useful tool for quantifying the effectiveness of the shock absorber itself in dissipating energy. The reduction of these time-dependent ratios occasionally observed for specific earthquake time ranges reveals that adverse frequencies are occasionally present in seismic excitation and allows for the identification of the optimal damping coefficient.