In an ultrasonic welding apparatus comprising an ultrasonic sonotrode and a backing plate, flat workpieces to be welded are pressed between the sonotrode and the backing plate. Projections are provided on a portion of the surface of the sonotrode and on a portion of the surface of the backing plate, each projection-bearing surface portion being adjoined by a smooth portion. The flat workpieces are for example ends of a strapping tape formed in a loop around a package in a strapping machine and the aim is to produce a weld of increased strength.