The invention provides an adapter for a dental milling block holder with a dental milling block (52 and 54) or dental grinding block, which is attached to a dental milling block holder, in particular glued on, wherein the dental milling block holder is provided with a round shank which is mounted in the adapter (40). It is characterized in that the adapter (40) is provided with at least one internal thread (92) for the mounting of a fastening screw (31) which acts on the shank, to which fastening screw (31) inside the shank mount of the adapter (40) of the fastening screw (31) positioned opposite of it, at least one in particular elevated, in particular at least two elevated clamping surfaces (74 and 76) are formed against which the shank abuts.