610234 A teatcup liner (2) for a teatcup (1) to be attached to a teat of an animal in a milking operation is disclosed. The teatcup liner (2) is composed of at least three separate annular sections (11-13), which are attached to each other and arranged successively along the longitudinal centre axis (x). The three sections include a first section (11) having an opening for allowing the teat to be introduced into the inner space, a second section (12) forming a tube part (16) to engage the teat during the milking operation and a third section (13) forming a ring module. The ring module has an inner surface facing the inner space and comprises a functional member (40) which provides an additional function to the milking operation. The sections (11-13) are engageable with each other interchangeably to allow various configurations of teat cup liners (2) to be manufactured from compatible sections.