In the Italian media, the heavy rain is called a water bomb - streets in villages and smaller towns have been completely flooded in the Anconca region.
Among the missing are two children, according to Italian Rai.
One of the children was swept away by the waters as his mother tried to get out of her flooded car.
In some parts of the region, 400 millimeters of water has fallen, which corresponds to a third of the normal amount of rain in a year, writes La Stampa.
Of the victims, several drowned when their cars filled with water.
In the city of Senigallia, the river Misa has flooded and pictures from the scene show how the rescue service is rescuing people with the help of rubber boats.
In several places, schools are closed and electricity and telephone connections have stopped working.