An empirical method to correlate and to predict the vapor-liquid equilibria of several amorphous polymers in polar and nonpolar solvents is proposed. The method mainly consists of a simple modification of the entropic term of the Flory-Huggins equation which follows from the free-volume dissimilarity concept. Further, the enthalpic contribution to the excess Gibbs energy is calculated through the NRTL equation according to a previous work by the author. The only input parameters required to apply the method are the liquid molar volume of the solvent and the density of the polymer. Two empirical correlations are proposed to calculate the corrective factor of the entropic term for systems containing cyclic and noncyclic solvents, respectively. Further, according to a previous strategy applied to predict the VLE of the usual liquid mixtures, the whole corpus of literature data is subdivided into five classes, each of them deserving "ad hoc" rules to evaluate the binary constants of the NRTL equation. From the analysis reported in this work it results that the enthalpic term is relevant only for some of the above classes of mixtures, while the nonideality of the remaining ones can be described by the entropic term only. The proposed method is evaluated on the basis of the prediction of the VLE data of 92 literature binary systems pertaining to the above classes. A comparison with some known predictive methods is also given.