Laboratory testing of fluid-saturated rock is often needed to properly duplicate field conditions, where pores in rock are filled with a liquid. It is desirable that laboratory specimens be fully saturated, because it reduces the number of unknown parameters and allows calculation of some of the rock's poroelastic moduli. However, full saturation is difficult to achieve in rock specimens because of the air bubbles trapped in pores. In order to dissolve air bubbles, back pressure can be applied to the specimens, decreasing the size of air bubbles and reducing the time needed to dissolve them in water. A process to saturate Berea sandstone is presented. Skempton's B coefficient was measured at each increment of back pressure while keeping the effective mean stress approximately the same. A B-value that was constant and independent of the magnitude of the back pressure indicated full saturation. The maximum B achieved for the sandstone at 5 MPa effective mean stress was 0.58. This value was confirmed by calculation of Skempton's coefficient from other poroelastic parameters. Moreover, full saturation was assured by the measurement of a constant P-wave velocity with increasing back pressure.