The　protection　of　rigid　block-like　structures　against　seismic　hazards　is　a　widely　studied　topic　and　has　been　achieved　to　different　degrees　with　active　and　passive　protection　methods.　For　the　protection　of　rigid　block-like　structures,　this　paper　proposes　the　coupling　of　a　rigid　block-like　structure,　modelled　as　a　single　rigid　block,　with　an　external,　auxiliary　system　through　a　hysteretic　elasto-plastic　device.　The　auxiliary　system　is　constituted　by　an　oscillating　mass,　whose　inertial　effects　are　amplified　by　the　use　of　an　inerter　device.　The　auxiliary　system　works　as　a　hysteretic　mass　damper.　The　elasto-plastic　behaviour　of　the　coupling　device　is　described　by　the　Bouc-Wen　model.　The　mechanical　model　of　the　coupled　system　has　two　degrees　of　freedom,　and　its　equations　of　motion　can　be　written　by　following　a　direct　approach.　A　preliminary　analysis　is　performed　by　exciting　different　coupled　systems　and　the　corresponding　stand-alone　rigid　blocks　with　harmonic　base　accelerations.　Such　an　investigation　is　aimed　at　understanding　the　sensitivity　of　the　dynamics　of　the　coupled　systems　to　the　characteristics　of　the　rigid　blocks　and　auxiliary　systems　and　is　performed　by　comparing　the　frequency-response　curves　of　the　coupled　systems　with　those　of　the　corresponding　stand-alone　rigid　blocks.　A　further　analysis　is　performed　to　verify　the　effectiveness　of　the　proposed　protection　methodology　under　seismic　excitation.　Both　the　harmonic　and　seismic　analyses　show　that　the　main　parameter　to　be　tuned　to　achieve　the　protection　of　the　rigid　block-like　structures　is　the　apparent　mass　of　the　inerter　device.　A　proper　choice　of　such　a　mass　improves　the　dynamics　of　the　rigid　block-like　structures,　leading　to　smaller　oscillations　for　the　same　level　of　excitation.