A milk collecting piece comprises a kink element having a bending edge which ensures reliable kinking and thus maintenance of the operating vacuum in milk tubes which are guided outwards in a direction oblique to the longitudinal axis. In one embodiment, the milk collecting piece comprises a connection surface provided with an opening into which an end portion of the milk tube is introduced, so that a reliable function is obtained due to the provision of the kink element, whereby due to the manner in which the milk tube is mounted on the collecting piece, a smaller amount of milk coating collects and deposits on transition areas. In a further embodiment, the bending edge of the kink element is positioned in such a manner that said edge efficiently prevents the milk tube from getting detached from connection elements which are guided outwards in an oblique manner, and ensures vacuum-tight kinking of the milk tube at the same time. Furthermore, a kink element is described which is to be fastened in a simple manner or with only slight constructional modifications to already existing milk collecting pieces.