Nanostructured Cu–Ni alloys have become the focus of public attention due to their better corrosion resistance and high hardness in experimental measurements. First-principles calculation based on the density functional theory (DFT) has been confirmed as an effective tool and used to illustrate the mechanical properties of these alloys. In this paper, the DFT has been employed to calculate the mechanical properties of Cu–Ni alloys, including bulk modulus, shear modulus, Young’s modulus, anisotropic index, Poisson’s ratio, average velocity, and B/G. We find that the Ni-rich Cu–Ni alloys have relatively higher mechanical parameters, and the Cu-rich alloys have smaller mechanical parameters, which is consistent with previous experiments. This provides an idea for us to design alloys to improve alloy strength.