In an arrangement for recreating a model, use is made of an original model (1) of implant and/or tooth remnants (2-5) in a system for producing a dental construction (32). The system includes a reading apparatus (10, 13) and a first levelling function (6). A reproduction of all or part of the original model is created in CAD equipment. The said dental construction is created in the CAD equipment, and the reproduction and the construction are divided up into parts whose axes of inclination and contact surfaces are identified in terms of position and direction. Replicas of the implant and/or tooth remnant parts and the construction parts are produced and mounted on a mounting member (23) after bore holes for the replicas of the tooth remnant parts have been established using boring equipment. The said bore holes are established by means of a second levelling function and the bore holes receive positions and longitudinal axis inclinations which correspond to the positions and the inclinations of corresponding axes in the original model. The replicas for the tooth remnant parts can be fixed in terms of angle of rotation in the mounting member with position-fixing members (identification members). The last-mentioned replicas form the recreated model on which the construction replicas can be applied.