A　coupled　thermo-mechanical　3D　finite　element　model　is　developed　to　simulate　the　cogging-down　rotary　swaging　(RS)　processing　of　pure　magnesium　square　billet　in　this　paper.　Through　simulation,　the　effects　of　high-frequency　pulse　stroking,　special　to　RS,　on　the　distributions　and　histories　of　different　field-variables　such　as　stress,　strain,　temperature　and　so　on　are　clarified.　The　effect　of　the　cogging-down　RS　on　the　subsequent　RS　passes　is　also　analyzed.　It　is　shown　that　the　strain　of　each　node　increases　stepwise　with　pulse　stroking.　The　equivalent　strain　of　nodes　at　the　corner　of　the　square　billet　is　much　higher　than　that　at　the　center　by　1.48.　The　stresses　fluctuate　periodically　with　the　pulse　stroking.　The　axial　component　sigma(z)　of　the　residual　stress　at　the　corner　of　the　cogging-down　RS　bar　is　as　high　as　32　MPa　that　it　becomes　one　of　the　main　factors　causing　the　transverse　surface　crack　in　the　subsequent　RS　passes.　The　temperature　rising,　owing　to　the　heat　translation　from　plastic　deformation　energy　is　only　1　degrees　C　in　the　cogging-down　RS.　Compared　the　calculated　results　with　experimental　data,　the　consistency　is　demonstrated.　(c)　2007　Published　by　Elsevier　B.V.