Compressional- and shear-wave velocities of water-saturated Berea sandstone have been measured as functions of confining and pore pressures to 2 kbar. The velocities, measured by the pulse transmission technique, were obtained at selected pressures for the purpose of evaluating the relative importance of confining pressure and pore pressure on elastic wave velocities and derived dynamic elastic constants. Changes in Berea sandstone velocities resulting from changes in confining pressure are not exactly canceled by equivalent changes in pore pressure. For properties that involve significant bulk compression (compressional-wave velocities and bulk modulus) an incremental change in pore pressure does not entirely cancel a similar change in confining pressure. On the other hand, it is shown that a pore pressure increment more than cancels an equivalent change in confining pressure for properties that depend significantly on rigidity (shear-wave velocity and Poisson's ratio). This behavior (as well as observed wave amplitudes) is related to the presence of high-compressibility clay that lines grains and pores within the quartz framework of the Berea sandstone.