Method of, and apparatus for, sinking bore holes, in particular exploratory and extraction bore holes, in the sea bed (40). The material from the sea bed is loosened with the aid of a rotating drill head (10) which is arranged at the bottom end of a drill string (5) which is suitable for transmitting a torque. The top end of the drill string is mounted on a floating platform (1), it being the case that the drill string (5) comprises at least two telescopically interengaging drill-string parts (6, 7) which, during a vertical movement of the platform, induced for example by the sea swell, execute a movement relative to one another, with the result that the drill head (10) rests with an essentially constant force on the surface which is to be cleared away.