A method for determining a volume or a mass of a filling material is provided, in which firstly an empty profile detection mode is assumed in the absence of a filling material, and then a volume or mass determination mode is assumed when the filling material is present. In the empty profile detection mode, an interference point profile is created from echo curves obtained by scanning a container surface. The interference point profile is then taken into account when determining the volume or the mass of the filling material in the volume or mass determination mode, such that volumes or masses of the filling material are determined with increased accuracy.