[en] The ANTARES neutrino telescope is presently being built in the Mediterranean Sea at a depth of 2500 m. The primary aim of the experiment is the detection of high energy cosmic muon neutrinos, which are identified by the muons that are produced in charged current interactions. These muons are detected by measuring the Cherenkov light which they emit traversing the detector. Sometimes a high momentum muon produces electromagnetic showers. The subject of this paper is a method to reconstruct these showers which includes several steps: an algorithm for the fit of the muon track parameters, preselection of detected photons belonging to a shower, and a final fit with the preselected detected photons to calculate the electromagnetic shower position. Finally a comparison between data obtained with that part of the detector that is currently in operation and simulations is presented