EOS is an analytical equation of state which models high pressure theory and fits well to the experimental data of ∊-Fe, SiO2, Mg2SiO4, and the Earth. The cold part of the EOS is modeled after the Varpoly EOS. The thermal part is based on a new formalism of the Gruneisen parameter, which improves behavior from earlier models and bridges the gap between elasticity and thermoelasticity. The EOS includes an expanded state model, which allows for the accurate modeling of material vapor curves.