In　this　paper,　effective　models　have　been　developed　to　simulate　the　mechanics　states　of　specimens　during　stretch　and　un-stretch　grinding,　by　the　thermal　elastic-plastic　finite-element　method.　The　results　of　calculations　show　that　stretch　grinding　can,　under　certain　conditions,　very　effectively　reduce　the　residual　tensile　stress　in　the　surface　layer　of　the　workpiece　or　even　convert　the　residual　tensile　stress　into　residual　compressive　stress,　Through　analysis　of　the　present　results,　the　mechanism　of　the　reduction　of　residual　tensile　stress　by　stretch　grinding　is　revealed.　(C)　1999　Published　by　Elsevier　Science　S.A.　All　rights　reserved.