Cultural objects of archeological findings are often broken and fractured into a large amount of fragments, and the archeologists are confronted to 3D puzzles when reassembling the fractured objects. Scanning the fragments and reassembling the corresponding 3D objects virtually is an elegant (and sometimes the only) solution. During the assembly, an efficient user interaction for the complex task to orientate or position two 3D objects relative to each other is essential. Even though fully automatic assembly methods based on pairwise matching exist, they fail when some fragments are flawed or missing. Consequently, an efficient user interaction is always equired, in addition to automatic techniques. In this paper, we present ArcheoTUI, a new tangible user interface for the efficient assembly of the 3D scanned fragments of fractured archeological objects. The key idea is to use tangible props for the manipulation of the virtual fragments. In each hand, the user manipulates an electromagnetically tracked prop, and the translations and rotations are directly mapped to the corresponding virtual fragments on the display. For each hand, a corresponding foot pedal is used to clutch the movements of the hands. Hence, the hands of the user can be repositioned, or the user can be switched. The software of ArcheoTUI is designed to easily change assembly hypotheses, beyond classical undo/redo, by using a scene graph. We designed ArcheoTUI on the demand of archeaologists and in a direct collaboration with them, and we conducted a user study on site at their workplace. This user study revealed that the interface, and specially the foot pedal, was accepted, and that all the users managed to solve simple assembly tasks. In a case study, we show the assembly of one of their fractured archeological findings.