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We report compressive mechanical response of graphene foams (GFs) and the thermal resistance (RTIM) between copper (Cu) and GFs, where GFs were prepared by the chemical vapor deposition method. We observe that Young’s modulus (EGF) and compressive strength (σGF) of GFs have a power law dependence on increasing density (ρGF) of GFs. The maximum efficiency of absorbed energy (ηmax) for all GFs during the compression is larger than ∼0.39. We also find that a GF with a higher ρGF shows a larger ηmax. In addition, we observe that the measured RTIM of Cu/GFs at room temperature with a contact pressure of 0.25 MP applied increases from ∼50 to ∼90 mm2 K/W when ρGF increases from 4.7 to 31.9 mg/cm3.