The submarine played an active part in military operation during the last of nineteenth century. Today, as an aid to science and technology and technology m the submarine is being utilized in the fields of deep sea investigation and sight-seeing as well as military activities. When the stability and the maneuverability of a submarine is studied, the problems arise on the vertical plane as well as the horizontal plane. However, the horizontal plane has been dealt with in the study of surface vessels. The author attempts to look into the hydrodynamic directional stability at high speeds (above 10knots) on the vertical plane, and to clarify the submarine's depth-rate as related to the factors that affect it : the distance from the center of buoyancy to the center of gravity, the speed of the submarine, and the position and the area ratio of hydroplane. In this study, the author considered the two groups of dimensionless derivatives of submarine. It is confirmed that the depth-rate of a submarine is decreased when the length, of BG is increased under the continuous submerging status. But the depth-rate is increased when the area ratio of hydroplane is enlarged. It is also confirmed that a submarine has only one critical speed in accordance with the shape of its hull, but unconcerned with its speeds.