Abstract: For the drilling of bore holes there is provided an assembly of drilling machine elements which are positioned on top of each other and which include a gripping body comprising of two or more shells between which are positioned expanding-contracting cylinders for causing the shells to be pressed against the wall of a hole being drilled, a hollow drive shaft and a drilling tool being suspended below the gripping body. In addition to the above mentioned gripping body which acts outwardly of the center of the assembly, there are provided gripping plates which act radially inwardly of the hollow drive shaft to grip the stem of the drilling tool, which extends within the hollow drive shaft.