We model the location, geometry and density of the source of the recent geological unrest at Campi Flegrei caldera (Italy) by inverting levelling, trilateration and gravity measurements collected between 1980 and 1995. The best fitting source for the 1980--84 inflation is a horizontal penny-shaped crack with a density 142 to 1115 kg/m3. The source best fitting the deflation period (1990--95) is a vertical spheroid with density between 902 and 1015 kg/m3. These results exclude the intrusion of magma, and indicate the migration of fluid to and from the caldera hydrothermal system as the cause of ground deformation and consequent unrest.