Cu has been used extensively to replace Al as interconnects in ULSI and MEMS devices. However, because of the difference in the thermal expansion coefficients between the Cu film and the Si substrate, large biaxial stresses will be generated in the Cu film. Thus, the Cu film becomes unstable and even changes its morphologies which affects the device manufacturing yield and ultimate reliability. The structural stability and theoretical strength of Cu crystal under equal biaxial loading have been investigated by combining the MAEAM with Milstein-modified Born stability criteria. The results indicate that, under sufficient tension, there exists a stress-free BCC phase which is unstable and slips spontaneously to a stress-free metastable BCT phase by consuming internal energy. The stable region ranges from −15.131 GPa to 2.803 GPa in the theoretical strength or from −5.801% to 4.972% in the strain respectively.