This paper looks at polymer-solvent phase behavior at conditions near the solvent vapor pressure curve where vapor-liquid-liquid equilibria can occur. Data of Kennis (1988) and Kennis et al. (1990) for a high-density polyethylene in n-hexane have been modeled using the Sanchez-Lacombe lattice gas model, the related mean-field lattice gas model of Kleintjens and Koningsfeld (1980), and the perturbed hard-sphere-chain (PHSC) model of Song et al. (1994a,b). Phenomena of interest include LCST behavior and the liquid solvent, vapor solvent, polymer three-phase condition. Some aspects of the computational problems are described in the paper. These include such matters as the relationship between the spinodal and the coexistence curves and the potential for locating metastable liquid-liquid equilibria at conditions near the solvent vapor pressure curve. Convergence of flash calculations proves to be problematic, with the vapor-liquid equilibria and liquid-liquid equilibria showing somewhat different character. Some techniques are described for modifying the familiar successive substitution computational algorithm so that convergence can be obtained.