The statistical associating fluid theory of variable range employing a Mie potential (SAFT-VR-Mie) proposed by Lafitte et al. (J. Chem Phys. 2013, 139, 154504) is one of the latest versions of the SAFT family. This particular version has been shown to have a remarkable capability to connect experimental determinations, theoretical calculations, and molecular simulations results. However, the theoretical development restricts the model to chains of beads connected in a linear fashion. In this work, the capabilities of the SAFT-VR Mie equation of state for modeling phase equilibria are extended for the case of planar ring compounds. This modification proposed replaces the Helmholtz energy of chain formation by an empirical contribution based on a parallelism to the second-order thermodynamic perturbation theory for hard sphere trimers. The proposed expression is given in terms of an extra parameter, chi, that depends on the number of beads, m(s), and the geometry of the ring. The model is used to describe the phase equilibrium for planar ring compounds formed of Mie isotropic segments for the cases of m(s) equals to 3, 4, 5 (two configurations), and 7 (two configurations). The resulting molecular model is further parametrized, invoking a corresponding states principle resulting in sets of parameters that can be used indistinctively in theoretical calculations or in molecular simulations without any further refinements. The extent and performance of the methodology has been exemplified by predicting the phase equilibria and vapor pressure curves for aromatic hydrocarbons (benzene, hexafluorobenzene, toluene), heterocyclic molecules (2,5-dimethylfuran, sulfolane, tetrahydro-2H-pyran, tetrahydrofuran), and polycyclic aromatic hydrocarbons (naphthalene, pyrene, anthracene, pentacene, and coronene). An important aspect of the theory is that the parameters of the model can be used directly in molecular dynamics (MD) simulations to calculate equilibrium phase properties and interfacial tensions with an accuracy that rivals other coarse grained and united atom models, for example, liquid densities, are predicted, with a maximum absolute average deviation of 3% from both the theory and the MD simulations, while the interfacial tension is predicted, with a maximum absolute average of 8%. The extension to mixtures is exemplified by considering a binary system of hexane (chain fluid) and tetrahydro-2H-pyran (ring fluid).