Forming characteristics for the bundle extrusion of Cu-Ti bimetal wires are investigated, which can identify the process conditions for weak mechanical bonding at the contact surface during the direct extrusion of a Cu-Ti bimetal wire bundle. Bonding mechanism between Cu and Ti is assumed as a cold pressure welding. Then, the plastic deformation at the contact zone causes mechanical bonding and a new bonding criterion for pressure welding is developed as a function of the principal stretch ratio and normal pressure at the contact surface by analyzing micro local extrusion at the contact zone. The averaged deformation behavior of Cu-Ti bimetal wire is adopted as a constitutive behavior at a material point in the finite element analysis of Cu-Ti wire bundle extrusion. Various process conditions for bundle extrusions are examined. The deformation histories at the three points, near the surface, in the middle and near the center, in the cross section of a bundle are traced and the proposed new bonding criterion is applied to predict whether the mechanical bonding at the Cu-Ti contact surface happens. Finally, a process map for the direct extrusion of Cu-Ti bimetal wire bundle is proposed.