With the rapid development of the electronics industry, high-density electronic devices and component mounting have gained popularity. Because of the heat generated from these devices, efficiency of the electronic parts is significantly lowered and life of various electronic devices is considerably shortened. Therefore, it is essential to efficiently dissipate the heat generated from the device to extend product life and ensure high efficiency of electronic components. This study evaluated how residual stress is impacted by the thickness of the deposited copper film, which is widely used as a heat dissipation material, and the number of graphene layers. The results confirmed that the residual stress decreased with increasing thickness. Moreover, the residual stress changed based on the transfer area of graphene, which had an elastic modulus eight times that of copper, indicating that the residual stress of the deposited copper film can be controlled.