A process is disclosed for overmolding crosslinked tubing ends onto a crosslinkable tube. The tube, made of a first polymer, has an inner diameter. The tube is inserted at least partially into a mold and at least partially onto a cylindrical mandrel having a base and a tip. The mandrel has an outer diameter dimensioned to allow the inner diameter of the tube to slide thereon. The mold contains a void for injection of a second polymer. The void co-acts with the mandrel and the tube to define an overmolding shape. After injection molding the second polymer over the tube and the mandrel in the void of the mold, the first and second polymers are crosslinked. Different embodiments of the overmolding shape are taught.