A lip member of a teatcup liner for a teatcup includes a first end (3a) turned towards an udder of an animal to be milked a second end (3b) turned away from the udder a longitudinal center axis (x) extending through the first end and the second end an annular base (60) extending around the longitudinal center axis and a lip (61) with a lip edge (62) defining an opening for receiving a teat of the animal, the lip extending inwardly from the annular base towards the longitudinal center axis to the lip edge and having an oscillating shape with a plurality of oscillations seen radially from the longitudinal center axis, each oscillation including a peak portion (63) and valley portion (64), where the lip, at least in the rest state, slopes from the annular base towards the second end.
