This paper presents an investigation on the anisotropic modulus of energetic crystals of b-HMX by using a Hysitron Triboindenter fitted with a Berkovich tip. High quality single crystals of b-HMX, whose densities were determined by high precision density gradient tube (DGT), were used in order to extract the moduli of two orthogonal crystal faces: (010), the maximum growth habit face (termed face 1), and the face which is perpendicular to it (termed face 2). Contrary to common expectation, the moduli of face 1 and face 2 were found to be 23.4 and 26.1 GPa, respectively, indicating a negligible crystal anisotropy of the system. Nanoindentation measurement gave even narrower difference, with hardness values of 1.1 GPa for face 1 and 0.95 GPa for face 2, thus further supporting the above conclusion. The result obtained from nanoindentation contradicts with those from the impulse stimulated light scattering (ISLS) and the Brillouin scattering, but was close to the result predicted by molecular dynamics (MDs) simulation. It is also suggested that the modulus value of 31 GPa obtained from previous micro-indentation measurement may be overestimated.