A teatcup to be attached to the teat of an animal and a teatcup liner (1) for mounting in a shell (2) of the teatcup, where the teatcup liner includes a barrel (3) enclosing an inner space (7) for receiving the teat. The barrel includes a lower section (3′) and an upper section (3″) adjoining the lower section. The barrel has a polygonal cross-sectional shape, defining a plurality of side portions (18) and a plurality of corner portions (19), each connecting two of the side portions. Each side portion has a side wall thickness at a center line of the side portion. Each corner portion has a corner wall thickness at a center line of the corner portion. The corner wall thickness is thicker than the side wall thickness along the barrel. The corner wall thickness decreases along the upper section of the barrel towards the lower section.