Apparatus for removing milk from a teat of an animal comprising an outer body having an opening into which the teat is insertable into a space defined by two or more resilient membranes. A pressure difference is applied between the space between the resilient membranes and a region outside the membranes to cause the membranes to ball on to the teat, thereby massaging it to extract milk. To avoid exerting excessive force on the end of the teat yet retain a useful massage pressure, the resilient membranes are under tension in a direction transverse to the direction of teat insertion before the provision of any pressure difference (before the insertion of the teat).