In order to further understand the similarity and difference between deformation mechanisms of single crystals and poly-crystalline
materials, the influence of external constraint and rolling geometry on the deformation behaviour of copper single crystals with {123}<634> orientation was investigated by embedding them into metal frames of different strengths. The metal frames were made of aluminum and mild steel, respectively. The results show that the
deformation banding degree of the crystal increases with the strength of metal frame and shear strain. For the crystals rolled under lower γg (γg is the ratio of the geometrical redundant shear strain to the normal rolling strain), the deformation is homogeneous. For the crystals rolled under higher γg, the deformation is extremely inhomogeneous. The deformation is more homogeneous in the crystals rolled in steel frames than that rolled in aluminum frames. The S-orientation is more stable in the crystals rolled under lower γg than that rolled under higher γg.