We present here phase equilibria calculations of polyethylene solutions in different solvents as obtained with two versions of the SAFT equation of state, soft-SAFT and PC-SAFT. The objective of this work is twofold: to check the accuracy of the soft-SAFT equation in providing reliable polymer solutions behavior and to propose a methodology from which systematic studies on polymer solutions can be made by the use of transferable molecular parameters. Some issues regarding the fitting of molecular parameters from polymer data as well as the numerical problems associated with polymer phase equilibria calculations are also mentioned. The methodology is applied to model the phase equilibria of polyethylene solutions with several solvents, differing in size and polarity, including n-pentane, n-hexane, butyl acetate, and pentanol, and results are compared to available experimental data. The phase behavior explored in this work is wide, from vapor-liquid equilibria to liquid-liquid equilibria, displaying upper critical solution temperatures and lower critical solution temperatures. We have also calculated the solubility of ethylene in polyethylene with the same models. Results obtained from the soft-SAFT equation are slightly more accurate in some of the cases than the PC-SAFT equation. Both equations, soft-SAFT and PC-SAFT, follow most of the experimental trends, providing accurate predictions from pure component parameters in some of the cases, while a binary interaction parameter was needed for the butyl acetate, 1-pentanol, and ethylene binary mixtures.