Isothermal-isobaric molecular dynamics (NPT-MD) simulations of the beta, alpha, and delta phases of crystalline 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX) were performed over the temperature range 4.2-553 K and 1 arm. The Buckingham repulsion-dispersion intermolecular potential developed for hexahydro-1,3,5-trinitro-1,3,5-s-triazine (RDX) (J. Phys. Chem. 1997, B101, 798) with electrostatic charges determined by ab initio calculations was used to describe the HMX crystal phases. The predicted space group symmetries and structural parameters for the three phases of HMX are in close agreement with experimental values.