A manipulator is operated for the motion of mechanical hands or arms. When a cup including liquid inside is shifted by a manipulator, it is important to know how a free surface of the liquid moves. In this study, non dimensional parameters have been found that affect the rise of the free surface in a cup moving with constant acceleration. The non-dimensional parameters are the dimensionless time, the ratio of inertia effect to viscous effect (the Reynolds number), the aspect ratio of the liquid inside the cup and the acceleration ratio (the Froude number). Through this study, the height of the free surface rise in a cup has been predicted and the detailed velocities in the liquid have been examined. Generally, the maximum rise of the free surface is dependent on the Reynolds number and Froude number strongly, but on the aspect ratio weakly. However, the influence of the aspect ratio on the maximum rise of the free surface is not negligible in the range of 10 < Re < 100.