The KM3NeT deep-sea neutrino telescope will use thousands of Digital Optical Modules (DOMs) forming a 3D array to detect the Cherenkov’s light produced by the particles generated after a neutrino interaction in the medium. The DOMs are arranged in Detection Units (DUs), structures anchored and maintained vertical by buoyancy each one containing 18 DOMs at different height. The DOMs are, thus, subject to movements due to sea currents. For a correct reconstruction of events detected by the telescope, it is necessary to monitor the position of each DOM with ~10 cm accuracy. For this, an Acoustic Positioning System (APS) with a piezo-ceramic transducer installed in each DOM and a long baseline of acoustic transmitters and receivers on the seabed is used. Besides, there is a system of compass/accelerometers in the DOMs to determine their orientation. Then, a mechanical model is used to reconstruct the shape of the DU taking as input the information from the positioning sensors and using the sea current velocity as free parameter of the DU Line Fit method. The mechanical equations consider the buoyancy and the drag force of any item in the DU line. This work describes the data process of the different sensors and systems to obtain the fit shape of DUs, the situation for the first DUs installed as an example and to study the viability and define the full process to apply in KM3NeT.