We investigate the performance of van der Waals (vdW) functions in predicting the elastic constants of beta cyclotetramethylene tetranitramine (HMX) energetic molecular crystals using density functional theory (DFT) calculations. We confirm that the accuracy of the elastic constants is significantly improved using the vdW corrections with environment-dependent C-6 together with PBE and revised PBE exchange-correlation functionals. The elastic constants obtained using PBE-D3(0) calculations yield the most accurate mechanical response of beta-HMX when compared with experimental stress-strain data. Our results suggest that PBE-D3 calculations are reliable in predicting the elastic constants of this material.