Instrumentation has been developed to conduct Brillouin scattering measurements on small (0.15 mm) transparent single crystals at hydrostatic pressures up to 35 kilobars in a gasketed diamond anvil cell. Phonon velocities obtained this way can be used to calculate elastic moduli as a function of pressure. Results of measurements made on NaCl yield zero-pressure values of c11=4.82×1011 dyn cm−2, c12=1.28×1011 dyn cm−2, and c44=1.27×1011 dyn cm−2. The plots of the elastic moduli versus pressure are fitted with straight lines with the following slopes: ∂c11/∂P=11.62, ∂c12/∂P=3.05, and ∂c44/∂P=0.759.