The Ni-based superalloys are widely used for equipments operating at high temperatures. The prediction of their deformation behaviors will be very useful in understanding existing alloys and designing new alloys. In this study, the effects of alloying elements (Al, Co, Cr, Cu, Fe, Hf, Mo, Nb, Pt, Re, Ta, Ti, W, Y and Zr) on the elastic constants (c_ij’s) of Ni have been investigated using the first-principles calculations within the generalized gradient approximation. The supercells with 31 Ni atoms and one alloying atom were used. The calculated bulk modulus and shear modulus are compared with the available experimental data and analyzed based on the volume changes and electron density of the Ni-X dilute solutions. The addition of Y, Zr and Hf results in larger decrease of elastic moduli of Ni with respect to other alloying elements studied herein, which are traceable to the larger increase of volume. The solid solution strengthening on Ni caused by the addition of alloying elements is also studied. The melting temperatures of Ni-X dilute solutions obtained from the available thermodynamic databases have been compared to those obtained from the empirical relationship with the elastic constant c₁₁.