Calculations have been carried out on a model of electrolyte solutions with the following features: (i) the ions of the strong binary electrolyte are distributed in a lattice-like arrangement, (ii) ions are immersed in an incompressible, structure-less, continuous dielectric but this medium has a dielectric gradient in the vicinity of ions due to the polarizing effect of their electric field, (iii) coulombic interaction is calculated with respect to an average dielectric “constant” depending on the interionic separation distance, and (iv) the dielectric gradient regions around the ions result in a repulsive force between ions due to the work required to remove solvent from the dielectric gradient region when lowering the interionic separation distance. Comparison of calculated and observed data for the average dielectric constant, mean ionic activity coefficients, and partial molar enthalpy contents of several 1–1 and 1–2 electrolytes shows fairly good agreement, in some cases in the entire concentration range, with no adjustable parameters involved.