We present a study of the pentaerythritol tetranitrate energetic material by means of the ab initio all-electron periodic Hartree–Fock quantum mechanical method with the STO-3G basis set. Our calculations yield the equilibrium lattice vectors a 0 and c 0 , the symmetry-preserving elastic constants (C 11 +C 12 ), C 33 , and C 13 , the bulk modulus B, and the linear moduli B a and B c . With regards to experiment, the average deviation of the calculated lattice vectors is 1% and that of the calculated elastic constants and moduli is 7.4%. In particular, the calculated bulk modulus 9.38GPa agrees with experiment within 4.8%.