First-principles density functional theory calculations have been performed to obtain constitutive relationships in the crystalline energetic material -cyclotetramethylene tetranitramine ͑-HMX͒. In addition to hydrostatic loading, uniaxial compressions in the directions normal to the ͕100͖, ͕010͖, ͕001͖, ͕110͖, ͕101͖, ͕011͖, and ͕111͖ planes have been performed to investigate the anisotropic equation of state ͑EOS͒. The calculated lattice parameters and hydrostatic EOS are in reasonable agreement with the available experimental data. The uniaxial compression data show a significant anisotropy in the principal stresses, change in energy, band gap, and shear stresses, which might lead to the anisotropy of the elastic-plastic shock transition and shock sensitivity of -HMX.