We present a study of the phase diagram for a hard sphere interaction site model of benzene using Monte Carlo computer simulation. The investigation considered the fluid phase and three types of solid phases. Two of these are similar to experimentally determined structures of benzene and the third is a structure which allows the system to reach a high packing density at high pressure through a columnar-like arrangement of the molecules. Extensive calculations of the solid and fluid thermodynamic properties were made. The results show that, for the solid phase, the structure which enables the closest packing of molecules is the most stable one. The solid structures similar to those of benzene, while apparently mechanically stable, were found to be thermodynamically metastable for this purely hard core system. The simulation results have been used to test the accuracy of the cell theory for the solid phase and an equation of state for the fluid phase due to Boublik, as well as phase diagram predictions obtained by using these approximations in combination.