To ascertain the fill level of vessels (10), mechanical vibrations are produced in a vessel wall (30) and the vibration pattern is analysed. The vibration is produced in a vessel wall (30) which is contacted by the contents to an extent which varies depending on the fill level, and the vibration pattern is then evaluated to discover to what extent the vessel wall (30) is contacted on the inside by the contents. For this, the decay time, the frequency, the intensity and/or the time integral of the intensity can be evaluated or the site of the maximum intensity of the mechanical vibrations in the vessel wall can be ascertained.