The NEMO Collaboration is involved in a long term R&D activity towards the construction of a km³ telescope in the Mediterranean sea. It has dedicated special efforts in the development of technologies for a km³ detector and in the search, characterization and monitoring of a deep sea site adequate for the installation of the Mediterranean km³. Now the NEMO Collaboration is involved in the Phase 1 of the project, planning to install a fully equipped deep-sea facility to test prototypes and develop new technologies for the detector. A full Monte Carlo simulation has been performed to analyse the response of a reduced-size detector to the passage of atmospheric muons. Preliminary steps of the simulation are presented in this work.