The　core　mission　to　establish　elastoplastic　constitutive　model　is　how　to　determine　the　magnitude　and　direction　of　plastic　strain　increment　for　material　under　the　given　load.　Fractional　derivative　provides　a　powerful　tool　for　determining　the　nonorthogonal　direction　of　a　certain　differentiable　function.　A　three-dimensional　(3D)　fractional　plastic　flow　rule　suitable　for　concrete　material　is　presented　for　the　first　time　utilizing　fractional　derivative.　The　direction　of　plastic　strain　increment　is　determined　by　the　proposed　fractional　plastic　flow　rule.　A　closed　form　yield　function　is　developed　in　the　transformed　stress　(TS)　space　based　on　the　nonlinear　unified　strength　criterion,　and　further　used　to　describe　the　plastic　strain　induced　by　hydrostatic　loading.　A　united　hardening/softening　function　proposed　by　the　authors　in　previous　works　is　adopted　to　describe　the　pre-peak　hardening　and　post-peak　softening　behaviour　of　concrete.　Furthermore,　a　3D　fractional　elastoplastic　constitutive　model　for　concrete　material　is　presented.　Only　nine　material　parameters　with　the　clear　physical　meaning　are　need　for　the　proposed　model,　and　the　determination　method　of　each　material　parameter　is　given.　A　series　of　test　results　of　concrete　with　different　strength　under　biaxial　and　triaxial　stress　conditions　are　used　to　assess　the　performance　of　proposed　model.　(C)　2019　Published　by　Elsevier　Ltd.