A method for operating a density measuring device having a measuring tube filled with the medium for determining the density of the medium, in which the measuring tube is incited to vibrate, the frequency of the vibration determined and the density of the medium being calculated from the determined frequency and other parameters which determine the physical-geometrical properties of the measuring tube. In particular, at least one mechanical stress of the measuring tube is determined, and with the obtained mechanical stress value, the influence of the mechanical stress of the measuring tube and/or the influence of the pressure in the medium on the determined density of the medium are or is—at least partially—taken into consideration or compensated.