Nowadays natural resources on shore have been almost exhausted all over the world and mankind is beginning searching for unexploited resources on the bed of deep-sea floor. In exploring mineral resources and etc. in the ground of sea-bed, a sumbersible craft is one of the most important tools. These days, the stage of the technique of building and operating an exploring submersible craft is almost alike that of building and operating an airplane in the first years of the nineteen-twenties. At the present time, the problems arising in building and operating a submersible craft can be divided into four parts as follows; 1. How to build a hull that can bear high pressure under deep sea level. 2. How to decide the necessary facilities to be put on it. 3. How to decide the scope of stabilities and maneuvering characteristics of it. 4. On what sea conditions, the devices of launching and recovering it should be designed on the mother-ship. In this paper treating one of the third problems the author made a mathematic formula that can be useful in deciding the scope of dynamic course stability on the vertical plane and actually calculated the onset speed of pitch instability of an exploring craft. With the above mentioned calculations the author demonstrated that the value of $Z_g$ and the speed of a submerged craft are the most important factors in decideing the scope of dynamic stability on the vertical plane.