The invention concerns an ultrasonic device for sealing at least two superimposed sheets, said device comprising a sealing assembly consisting of two elements which are respectively an anvil and a sonotrode, arranged opposite each other so that their facing surfaces form an interstice for passing through the sheets to be sealed, said interstice having an inlet section and an outlet section, the sonotrode vibrating at high frequencies to emit ultrasonic waves, characterised in that means are provided for generating between the superimposed sheets and said sealing assembly a relative movement along a specific feeding direction relative to the sealing assembly, and the section of said passage interstice decreases between its inlet section and its outlet section, and at least one element of said sealing assembly comprises a projecting ridge emerging into said passage interstice and extending along a direction globally parallel to said feeding direction. The invention also concerns a related method for sealing flexible packages, and the resulting packages.