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The variation of elastic properties, e.g., elastic constants, bulk modulus, and shear modulus of dilute Ni-base superalloys due to alloying elements (X's) and temperature, has been studied via first-principles calculations. Here, 26 alloying elements are considered: Al, Co, Cr, Cu, Fe, Hf, Ir, Mn, Mo, Nb, Os, Pd, Pt, Re, Rh, Ru, Sc, Si, Ta, Tc, Ti, V, W, Y, Zn, and Zr. It is found that (i) both the bulk and shear moduli of Ni-X decrease approximately linearly with increasing equilibrium volume, especially within each group of 3d, 4d, or 5d transition-metal alloying elements; (ii) all alloying elements considered herein increase the ratio of bulk to shear modulus (i.e., the ductility) and the elastic anisotropy of the Ni-X alloys; and (iii) the largest decrease of elastic properties of Ni is caused by alloying element Y. It is observed that the change of elastic properties of Ni due to various alloying elements is traceable from the distribution of (magnetization) charge density, for instance the spherical distribution of charge density facilitates shear deformation, resulting in a lower shear-related property. Using a proposed quasistatic approach based on the predicted elasticity-volume-temperature relationship, the isothermal and the isentropic elastic properties are predicted for the dilute Ni-X alloys at finite temperatures, displaying a decreasing trend with respect to temperature for each Ni-X system. Computed elastic properties are in favorable accord with available experimental data.