The dynamic behavior of the free surface of a liquid placed in rectangular or cylindrical containers, during a step transition from terrestrial conditions to weightlessness and liquid drainage from rectangular containers in zero gravity are investigated numerically. The required time for the surface oscillations to decay to 1% of the original amplitude was found to depend on Reynolds number and the contact angle. The numerically obtained results are shown to approach the exact zero-gravity equilibrium state asymptotically. During liquid drainage through a central hole, the degree of surface depression was found to depend strongly on the exit velocity. The amount of residual liquid could be reduced by strategically placing the exit ports at the lower corners of the tank.