Clad composite materials consist of stacks of different materials. During the extrusion process of clad composites, fracture of the sheath or core materials frequently occurs because of the discontinuity of deformation caused due to the differences in the flow stress of the sheath material and core material. In order to predict fracture of the sheath material with oxygen-free high conductivity copper, the theory of ductile fracture has been applied. The effect of lubrication behavior on fracture of core material has been investigated. A technique to predict the fracture strain rate has been proposed. The calculated interface bonding force between the core material and the sheath material has been used to assist in die design for the indirect and direct extrusion processes.