Abstract: A method of sinking a bore hole in underground formations which have at least one special stratiform formation which features vastly differing formation pressures in respect to a formation adjacent to it in the sinking direction and in which a drilling tool carried at the bottom end of a drill line and having a drill bit driven by a deep drilling motor drills out a first part of a bore hole which extends to a point close to the boundary area of the special formation, characterized in that upon subsequent sinking of a further part of the bore hole by the casing string which passes through at least one special formation, a tubular outer casing with a bottom end carrying a driven drill head is entrained, the bore hole being lined by this, at least in the region of the special formation.