A teatcup and a cartridge to be attached to a teat of an animal to be milked. The cartridge includes a sleeve having an upper end and a lower end, and a teatcup liner mounted in the sleeve and having an inner space for receiving the teat. A pulsation chamber is provided between an inner side of the sleeve and an outer side of the teatcup liner. The teatcup liner includes an upper end portion located at the upper end of the sleeve, a barrel portion and a lower end portion extending beyond the lower end of the sleeve. The lower end portion forms an end nozzle beyond the lower end of the sleeve. The end nozzle has a tapering external shape configured to be received in a milk conduit for transporting the milk from the cartridge to the milk conduit.