Measurements of the temperature and hydrostatic pressure dependence of the elastic constants of amorphous polycarbonate in the glassy state using high-resolution Brillouin spectroscopy are reported. It was found that the temperature and the pressure dependence of the longitudinal and the transverse sound velocity are strictly linear, in contrast to the behaviour found in polymethyl methacrylate (PM MA). A simple equation for the behaviour of the elastic constants c(11) and c(44), and the shear, Young’s and bulk modulus, can be given, which fits the experimental data well.