We present a computational study of hydrostatic compression effects on the pentaerythritol tetranitrate (PETN) energetic material up to 22.7 GPa by means of the ab initio all-electron periodic Hartree-Fock quantum mechanical method with the STO-3G Gaussian basis set. We fitted the calculated volume-energy relation to the energy SJEOS polynomial function from which we obtained the compression dependence of the pressure (P), the bulk modulus (B), and its pressure derivative (Y). We also fitted the experimental volume-pressure relation to the pressure SJEOS polynomial function, which allowed us to calculate the experimental bulk modulus (B-exp) and its pressure derivative (B'(exp)). Our calculated values, B = 6.73 GPa and B' = 24.63, are in reasonable agreement with the values B-exp = 8.48 GPa and B'(exp) = 14.42 from our fit to the experimental X-ray data and with the value B-exp = 9.8 GPa that was derived from the experimental elastic constants. In addition, we present a discussion on how the lattice vectors and the internal coordinates (i.e., bond lengths, bond angles, and torsion angles) of the C(CH2ONO2)(4) molecules in the PETN lattice change during hydrostatic compression of the crystal. Our calculated results suggest that the C(CH2ONO2)4 molecules cannot be considered as being rigid but are in fact flexible, accommodating lattice compression through torsions, bendings in their bond angles, and contractions in their bond lengths. At pressures higher than about 8 GPa, however, both the C(CH2ONO2)(4) molecules and the c lattice vector seem to stiffen somewhat. The a lattice vector does not exhibit this stiffening. As a consequence, the pressure dependence of the c/a ratio shows a minimum at about 8 GPa.