A molecular model based on the integral equation theory of statistical thermodynamics is used to study phase separation in PEG-salt aqueous two-phase systems. PEG molecules are modeled as hard spheres that attract each other through a temperature-dependent Yukawa potential, which mimics the effect of PEG-water hydrogen bonding on the attraction between PEG molecules. The salt ions are modeled as charged hard spheres interacting through a Coulombic potential. Excess thermodynamic properties due to Coulombic and Yukawa interactions are calculated by analytical solutions to the Ornstein-Zernike equation for the mean spherical approximation closure. Yukawa parameters for PEG-PEG interactions are determined by fitting the theoretical phase diagram for a pure Yukawa fluid to the experimental phase diagram for a PEG-water mixture. The model predicts experimentally observed trends : increasing the temperature increases the slope and length of the tie lines; increasing the PEG molecular weight increases the miscibility gap; and increasing the anion charge lowers the salt concentration at which phase separation occurs. Theoretical results allow us to infer the relative importance of ion-PEG interactions, ion-solvent interactions, and the interpenetrable able nature of PEG molecules on the phase separation in PEG-salt aqueous two-phase systems.