A methodology is presented for applying the Elliott-Suresh-Donohue (ESD) equation of state to polymer solutions based on knowledge of the polymer's molecular structure. Group contributions to the ESD shape parameter are presented for 88 functional groups to complement the existing group contribution methods for the solubility parameter and molar volume. Hydrogen-bonding contributions are treated explicitly through Wertheim's theory. The resulting extension provides a framework for solutions that may include any combination of small molecules, polymers, or intermediate compounds such as waxes and asphaltenes. As a demonstration, 20 polymer solutions are studied involving liquid and supercritical solvents exhibiting a range of phase behaviors. The polymers treated are polyethylene, polystyrene, polyisobutylene, poly(ethylene oxide), poly(propylene oxide), poly(vinyl acetate), poly(vinyl chloride), and poly(vinyl alcohol). Solvent partial pressures are generally correlated to high accuracy, but the accuracy for lower and upper critical solution behavior is only qualitative.