A method, and apparatus for performing the method, is provided for the purpose of forming and inserting seal pieces into a container cap of a type which comprises an integral cup-like member having a top panel, a skirt depending from the top panel, and a plurality of cap lugs formed in the rim and extending partially inward from the rim. A quantity of such caps is supplied onto a surface, preferably with the caps inverted resting on their top panels. The caps are gathered into a plurality of rows and forwarded to screw conveyor mechanisms for advancing the caps to seal inserting stations located substantially coplanar with said assembly surface. The screw conveyor mechanism includes a table with at least two slots therein and conveyor screws extending beneath and along the slots and carrying caps along the table to a discharge location where the caps are temporarily located. A supply strip of flexible seal material is directed into proximity to the inserting stations and precisely cut seal pieces from the strip are inserted into the caps.