First-principles density functional theory calculations have been performed with and without an empirical van der Waals (vdW) correction to obtain constitutive relationships of solid nitromethane under hydrostatic and uniaxial compressions. The unit-cell parameters at zero pressure and the hydrostatic equation of state at 0 K are in reasonable agreement with experimental data using pure DFT, and the agreement is significantly improved with the inclusion of the vdW dispersion correction. Uniaxial compressions normal to the {100}, {010}, {001}, {110}, {101}, {011}, and {111} planes were performed, and a comparison of the principal stresses, changes in energy, and shear stresses for different compression directions clearly indicate anisotropic behavior of solid nitromethane upon compression. The calculated anisotropic constitutive relationships might help to link the anisotropic shock sensitivity and the underlying atomic-scale properties of solid nitromethane.