A teatcup liner includes a head defining a mouthpiece, a barrel with an upper barrel joined to a lower barrel, an outlet portion that extends downward from the lower barrel co-operates with the shell of the teat cup. In a relaxed state, the barrel has a polygonal cross-sectional shape, with the lower barrel having a flexibility for closing during the liner collapse phase of the milking operation greater than a flexibility of the upper barrel such that corner portions of the lower barrel are weaker than the corner portions of the upper barrel thereby assuring the lower barrel collapses first to create an upward wave movement of the lower barrel towards the upper barrel that securely collapses the upper barrel onto the teat to provide an enhanced teat massage and relieve congestion in the teat tissue.
