The dielectric constant and the reflectivity of graphite under hydrostatic pressure are calculated in the photon energies from 0.6 to 1.0 eV. The Slonczewski-Weiss-McClure band model is employed together with the pressure derivatives of the band parameters given by Nagayoshi. The calculated lineshapes of the change of optical constants due to pressure are in good agreement with the observed ones by Misu et al. The trigonal warping in the band structure is found to play an essential role in the appearance of van Hove singularities in the joint density of states as well as in the determination of optical transition probabilities. It is also shown that the band parameter γ 1 and its pressure derivative give the dominant contribution to the position of structures and their pressure dependence in the optical constant spectra in the near infrared range.