A　tailing　dam　accident　can　cause　serious　ecological　disaster　and　property　loss.　Simulation　of　a　tailing　dam　accident　in　advance　is　useful　for　understanding　the　tailing　flow　characteristics　and　assessing　the　possible　extension　of　the　impact　area.　In　this　paper,　a　three-dimensional　(3-D)　computational　fluid　dynamics　(CFD)　approach　was　proposed　for　reasonably　and　quickly　predicting　the　flow　routing　and　impact　area　of　mud　flow　from　a　dam　failure　across　3-D　terrain.　The　Navier-Stokes　equations　and　the　Bingham-Papanastasiou　rheology　model　were　employed　as　the　governing　equations　and　the　constitutive　model,　respectively,　and　solved　numerically　in　the　finite　volume　method　(FVM)　scheme.　The　volume-of-fluid　(VOF)　method　was　used　to　track　the　interface　between　the　tailings　and　air.　The　accuracy　of　the　CFD　model　and　the　chosen　numerical　algorithm　were　validated　using　an　analytical　solution　of　the　channel　flow　problem　and　a　laboratory　experiment　on　the　dam-break　problem　reported　in　the　literature.　In　each　issue,　the　obtained　results　were　very　close　to　the　analytical　solutions　or　experimental　values.　The　proposed　approach　was　then　applied　to　simulate　two　scenarios　of　tailing　dam　failures,　one　of　which　was　the　Feijão　tailing　dam　that　failed　on　25　January　2019,　and　the　simulated　routing　coincided　well　with　the　in　situ　investigation.　Therefore,　the　proposed　approach　does　well　in　simulating　the　flow　phenomenon　of　tailings　after　a　dam　break,　and　the　numerical　results　can　be　used　for　early　warning　of　disasters　and　emergency　response.　©　2020.　This　work　is　distributed　under　the　Creative　Commons　Attribution　4.0　License.