New　advance　in　modelling　of　the　machining　process　is　of　great　significance　to　improve　component　performance　and　manufacturing　efficiency.　This　includes　the　material　constitutive　model　and　the　approach　used　to　describe　the　field　flow　of　the　material　in　cutting.　In　this　study,　a　3D　model　of　high　speed　machining　(HSM)　of　Ti6Al4V　titanium　alloy　is　developed.　The　coupled　Eulerian-Lagrangian　(CEL)　approach　was　used　to　simulate　the　proposed　cutting　model.　This　cutting　model　includes　a　proposed　constitutive　model　considering　the　strain　hardening,　strain-rate,　temperature　and　stress　state　(e.g.,　stress　triaxiality　and　Lode　parameter)　in　the　material　plasticity　and　damage.　This　machining　model　is　able　to　simulate　the　phenomenon　of　material　side　flow,　which　results　in　a　larger　chip　width　when　compared　to　the　width　of　cut　and　the　lateral　burr　formation.　The　phenomenon　of　material　side　flow　is　validated　by　experimental　results.　The　distribution　of　plastic　strain　and　stress　state　shows　that　the　workpiece　transforms　from　plane　strain　state　in　middle　surface　to　plane　stress　state　in　lateral　surface,　which　finally　results　in　the　formation　of　lateral　burr.　©　2021　The　Author(s).