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A recent hypothesis on the giant ship Syrakosia, built around 235 B.C under the rule of Jeron II of Syracuse, is presented. In this enterprise Archimedes was a minister or a supervisor of the architect (Archias from Corinth). Comparison is made about opinions on the possibilities Archimedes could have had to plan the ship and to foresee her stability properties. The reconstruction of the actual procedures available to him to evaluate volumes and centres of buoyancy of different solids is studied also with models of the volumes of the ship and of the geometric solids mentioned in the “Floating bodies”, to conclude that he could evaluate the stability properties on a quantitative basis only for the orthoconoid, the features of which were exhaustively studied in previous Archimedes’ works. Therefore he must have left to the architect the task of both planning and evaluating empirically the stability of the ship. The last propositions of the first book of the “Floating bodies” suggest that Archimedes may have taken the experience of the Syrakosia as a guideline to approach the problem of stability of sectors of spheres, as the ship was launched when the hull reached the floating line and then she was completed afloat. Stability features of these phases appear to be comparable to those of different portions of sectors of the same sphere as presented by Archimedes.