The majority of molecules which form liquid crystals are elongated in shape. However, disk shaped molecules have also been shown to exhibit liquid crystalline phases. In this paper we report a series of constant pressure Monte Carlo simulations of model discotic molecules. We have used the Gay-Berne potential, which is in essence an anisotropic version of a shifted Lennard-Jones potential, to model the interactions between the disks. Initially we studied a system of 512 molecules over a range of pressures to determine the mesophases formed and to construct the phase diagram. The system was found to exhibit isotropic, nematic, and columnar phases. We have also studied a larger system of 2000 molecules at a single pressure to calculate more accurately the distribution functions used to describe the translational and orientational order within the various phases.