The multi-tooth mandrel is used to machine the axially inner micro-grooved Copper tube ( AIGCT) ,and the geometric shape of the teeth directly affects the forming quality and the tool life. In this paper,based on both the characteristics of metal flow,which is presented by using the metallographic images of the rectangle tooth cross-section during the forming of AIGCT,and the boundary features of the forming zone of a single tooth,the forming zone is divided into four parts: rigid zoneⅠ,plastic deformation zone,rigid zone Ⅱand two compacted dead zones. Then,a mathematical model of the unit extruding force is established for the forming of tooth shape by means of the upper bound method,the mechanism of the process parameters affecting the unit extruding force is then analyzed,and the angle of optimal metal flow direction and the factors to influence the optimization are thus
solved. Finally,the parameters of tooth shape of the multi-tooth mandrel are optimized.