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By scattering from a variety of acoustic phonons, a complete stiffness tensor has been determined for crystalline β-HMX. The results are compared with recent experimental and theoretical determinations of the elastic constants and bulk modulus. Reasons for disagreement are discussed in terms of experimental limitations and anharmonic effects. The observed ordering of stiffness constants, C11 (18.4 GPa), C22 (14.4 GPa), and C33 (12.4 GPa), is qualitatively associated with physical phenomena including cleavage planes, patterns in crystal growth, and molecular packing. This interpretation is further corroborated by the linear compressibilities plotted in three crystallographic planes. The Voigt–Reuss–Hill bulk and shear moduli were found to be 9.9 and 3.7 GPa, respectively. The elasticity of b-HMX is also discussed in relation to proposed mechanisms for the initiation of detonation.