A method and an apparatus for ultrasonically welding plastic parts together. The ultrasonic welding apparatus includes: an air cylinder having a piston rod; an ultrasonic horn substantially rigidly coupled to an end of the piston rod and having a distal end; a rotary anvil having an axis of rotation generally perpendicular to an axis of the piston rod and comprising a periphery; a transducer for converting electric potential differences into ultrasound wave energy, the horn being acoustically coupled to the transducer; and drive means for causing the anvil to rotate. The distal end of the horn confronts the periphery of the anvil throughout rotation of the anvil. On one application, interlocked zipper strips are passed through a gap between the distal end of the horn and the periphery of the anvil. The anvil periphery has a plateau that presses the zipper against the distal end of the horn. The transducer is energized in synchronism with the plateau being opposed to the distal end of the horn.