The isotherms and elastic properties of β -HMX crystals were calculated through molecular simulations in NPT ensemble using COMPASS force field. The isotherms of β -HMX simulated were in reasonable agreement with experiments. The pressure-induced changes of the lattice parameters showed the anisotropic compression of β -HMX. The bulk modulus K₀ and its pressure derivative K₀′ were obtained by fitting the isotherms to different equations of state. However, the values of K₀ and K₀′ obtained from the isotherm are sensitive to the fitting forms of equations of state. The elastic constants and modulus were calculated by statistic analysis mode at different pressures in the range of 0~27 GPa. Cauchy pressure C₁₂-C₄₄ and G/K ratios were also calculated which indicated that β -HMX would become harder as the pressure increased, and as well the β -HMX elastic property transformed from brittleness to ductibility.