A teatcup (1) and a teatcup liner (3) for a teatcup to be attached to a teat of an animal for the performance of a milking operation. The teatcup liner defines an inner space for receiving the teat and a longitudinal center axis (x) extending through the inner space. The teatcup liner is composed of at least three separate annular sections, which are attached to each other and arranged successively after each along the longitudinal center axis. A first section (11) forms an upper part having an opening for allowing the teat to be introduced into the inner space. A second section (12) forms a tube part engaging the teat during the milking operation. A third section (13) forms a ring module having an inner surface facing the inner space. The ring module includes a functional member providing an additional function to the milking operation.
