In this paper, the authors theoretically investigate the sloshing of liquid in cargo oil tanks during ship oscillation, and evaluate the impulsive pressure caused by sloshing. Liquid motion in a cargo oil tank is limited by tank top plating. As soon as the upward motion of liquid surface relative to the tank is stopped, impulsive pressure occurs there. This phenomenon is sloshing of liquid. Limited motion of liquid surface can be determined approximately by omitting terms of higher order in Fourier series. Determining the impulsive velocity of liquid surface at the tank top plating, the impulsive pressure can easily be obtained by means of the semi-empirical formula given by Professor Watanabe, and is in good accordance with experimental results. Severe impulsive pressure is caused by severe liquid motion. Liquid motion depends not only upon the ratio of the period of oscillation of the tank and the gravest natural period of liquid oscillation, but also upon a parameter which is determined by the dimensions of the tank, the depth of liquid and the height of the center of oscillation. When the parameter takes a certain value, severe liquid motion never occurs even in case of resonance condition. Such a fact should be applied to control the impulsive pressure in cargo oil tanks.