We present density functional theory calculations of the extrinsic stacking fault energy γesf, twin fault energy γtf, and unstable stacking fault energy γusf of copper under large strains, up to ± 10%. The calculated values of γesf, γtf, and γusf for unstrained Cu are 41.8 mJ/m2, 20.2 mJ/m2, and 163.4 mJ/m2, respectively, in good agreement with experimental data and theoretical results. Four different types of strains are applied: (i) volumetric strain; (ii) uniaxial strain perpendicular to the fault plane; (III) uniaxial strains parallel to the fault plane; and (iv) shear strains across the fault planes. We find that γesf, γtf, and γusf are strongly dependent on the magnitude and type of strain, challenging the common conception that they are constant material properties. The predicted strong strain dependencies provide useful insight into the deformation mechanisms of copper under high pressure and shock conditions and provide essential data to improve current Cu empirical potentials.