Measurements of the elastic constants of single crystals of gold and gold-nickel alloys have been made by the ultrasonic pulse-superposition method at room temperature, with pressures varying from atmospheric to 10 Kbar. The values of the adiabatic elastic stiffnesses of gold obtained at atmospheric pressure are C=4.200, C'=1.473, and BS=17.28, in units of 1011 dyne/cm2. The pressure derivatives of the elastic constants of gold are dCdP=1.84, dC'dP=0.438, and dBSdP=6.15. The shear constants C and C' increase nonlinearly as a function of nickel concentration, whereas the bulk modulus, BS, decreases initially on alloying. The experimental results for dilute solutions were interpreted in terms of a model which assumes that the dominant contribution to C, C', and BS arises from gold-gold ion-core repulsive interactions. Using an exponential form for the ion-core potential, it was also possible to calculate the variation with composition of the shear constants for concentrated solutions. The ion-core contribution to the heat of formation was also calculated, and this appears to be in good agreement with the thermodynamic data. These results have led to an interpretation of the strain-energy term in alloy formation as arising from the changes in the short-range repulsive interaction between neighboring ions.