Thorium has long been considered a possible source of fuel for use in power generating nuclear reactors. While much attention and interest have focused on thorium oxide, metallic thorium alloys were investigated in the past as fuel candidates for fast and thermal breeder reactors. In this work, thorium’s two solid allotropes (face centered cubic α and body centered cubic β) are modelled using Density Functional Theory (DFT). The Vienna Ab Initio Simulation Package (VASP) is used to determine structural and elastic properties, as well as the density of states. The Voigt-Reuss-Hill approximations are used to predict the phases’ bulk moduli, shear moduli, Young’s moduli, and Poisson’s ratios. Four exchange-correlation potentials are used and compared. These are the LDA, the PBE-GGA, the RPBE, and the PBEsol. All potentials showed relatively good accuracy when predicting the lattice constant. The RPBE was the most accurate, slightly over predicting by < 0.2%. The RPBE and the PBE-GGA were the most accurate in predicting elastic properties, performing almost equally, while slightly over predicting most values.