Muon radiography represents an innovative tool for investigating the interior of active volcanoes. This method integrates the conventional geophysical techniques and provides an independent way to estimate the density of the volcano structure and reveal the presence of magma conduits. The experience from the pioneer experiments performed at Mt. Asama, Mt. West Iwate, and Showa-Shinzan (Japan) are very encouraging. Muon radiography could be applied, in principle, at any stratovolcano. Here we focus our attention on Vesuvius and Stromboli (Italy).