Constitutive relationships in the crystalline energetic material ␣-cyclotrimethylenetrinitramine ͑␣-RDX͒ have been investigated using first-principles density functional theory. The equilibrium properties of ␣-RDX including unit cell parameters and bulk modulus, as well as the hydrostatic equation of state ͑EOS͒, have been obtained and compared with available experimental data. The isotropic EOS has been extended to include the anisotropic response of ␣-RDX by performing uniaxial compressions normal to several low-index planes, ͕100͖, ͕010͖, ͕001͖, ͕110͖, ͕101͖, ͕011͖, and ͕111͖, in the Pbca space group. The uniaxial-compression data exhibit a considerable anisotropy in the principal stresses, changes in energy, band gaps, and shear stresses, which might play a role in the anisotropic behavior of ␣-RDX under shock loading.