The　post-earthquake　vertical　load-carrying　capacity　is　an　important　indicator　reflecting　the　traffic　flow　capacity　of　a　girder　bridge　after　an　earthquake.　However,　it　is　difficult　to　quantify　the　indicator　in　the　post-earthquake.　To　rapidly　assess　the　traffic　flow　capacity　of　a　bridge,　the　optimal　engineering　demand　parameter　(　EDP　)　for　post-earthquake　vertical　load-carrying　capacity　assessment　is　comprehensively　investigated　in　this　work.　Five　EDPs　related　to　the　residual　drift　and　the　damage　level　of　bridge　piers　are　first　selected.　Subsequently,　nonlinear　time-history　analysis　and　pushover　analysis　are　performed　for　RC　bridge　piers　considering　the　material　uncertainty　to　obtain　the　EDPs.　On　this　basis,　the　post-earthquake　vertical　load-carrying　capacity　for　RC　bridge　piers　with　residual　drift　and　damage　is　obtained　by　pushdown　analyses.　The　normal　cumulative　function　in　the　In　(x)　-y　coordinate　system　is　determined　as　the　optimal　model,　through　regression　analysis.　Based　on　the　performance　criteria　of　the　optimal　EDP,　an　assessment　on　the　optimal　EDP　of　post-earthquake　vertical　load-carrying　capacity　is　conducted.　The　findings　are　as　follows:(1)　The　optimal　EDP　is　the　maximum　drift　ratio　when　the　measurability　is　not　considered.(2)　The　residual　drift　ratio　is　determined　as　the　optimal　EDP　if　the　measurability　is　taken　into　account.　(　3　)　Taking　into　account　the　effect　of　aftershocks,　the　modified　Park-Ang　damage　index　is　the　optimal　EDP.　The　correlation　between　the　bridge　functionality　and　seismic　performance　can　be　established　by　the　optimal　EDP,　and　the　optimal　EDP　can　provide　references　for　further　development　and　improvement　of　the　seismic　resilience　assessment　and　the　seismic　design　of　bridges.　©　2024　Chinese　Society　of　Civil　Engineering.　All　rights　reserved.