Simulations of crystalline polyethylene are carried out at finite temperature and as a function of pressure. The equilibrium structures are obtained as those which minimize the free energy, calculated using an empirical force field for the interatomic potential and quasi-harmonic lattice dynamics for the vibrational free energy. The calculated pressure-volume equation of state at 300 K is in good agreement with the experimental results, and the reduction in volume with pressure (for pressures up to 2.5 GPa) arises almost entirely from a closer packing of the molecules rather than intramolecular effects. The pressure-induced frequency shifts of the infrared and Raman spectra are calculated, with the average error of the calculated shifts being 5 cm(-1)/GPa for the lattice modes and 2.6 cm(-1)/GPa for the internal modes. The frequencies of the A(g) scissor mode, the B-3u wag mode, and the A(u) twist mode decrease with pressure, while the other mode frequencies increase with pressure. The mode Gruneisen parameters decrease with pressure for the lattice modes and increase in magnitude with pressure for the internal modes (with one exception). The increase in the C-H stretching frequencies with pressure correlates linearly with the decrease in C-H bond lengths.