Multi-particle　dampers　(M-PD)　can　be　potentially　applied　in　civil　engineering　because　of　their　good　damping　effect　and　wide　frequency　band.　However,　because　of　their　complex　nonlinear　mechanical　properties　and　the　lack　of　a　reasonable　mechanical　model,　their　development　and　application　in　practical　engineering　are　limited.　Therefore,　without　considering　the　accumulation　of　particles,　an　equivalent　inertia　single-particle　mechanical　model　(EISM)　is　proposed　by　introducing　an　inerter　to　consider　the　effect　of　particle　rolling　on　the　damping　mechanism　and　performance.　Dynamic　analyses　of　the　EISM　single　degree　of　freedom　system　in　the　non-collision　stage　and　the　periodic　motion　after　collision　are　performed　based　on　the　analytical　solution.　The　influence　of　inertance　on　the　frequency　response　curve　of　dynamic　amplification　factors　in　the　no-collision　stage　and　the　analytical　solution　for　the　symmetric　two-impacts-per-cycle　motion　are　discussed　in　detail.　Numerical　simulations　and　experimental　verification　are　conducted　to　verify　the　rationality　of　the　above　theoretical　analysis.　The　results　show　that　EISM　can　further　clarify　the　nonlinear　characteristics　of　M-PD.　The　inertance　has　a　significant　influence　on　the　frequency　response　curve　of　the　dynamic　amplification　factors　as　well　as　the　boundary　conditions　and　stability　of　the　analytical　solution　of　the　symmetric　two-impacts-per-cycle　motion.　The　proposed　EISM　and　the　corresponding　theoretical　analysis　in　this　study　can　theoretically　support　further　analysis　of　the　vibration　reduction　mechanism　and　design　of　M-PDs.　©　2021　John　Wiley　&　Sons,　Ltd.