The invention relates to apparatus for milking animals such as cows, components of the apparatus and methods of milking animals employing the apparatus. The apparatus comprises at least two resilient membranes (18a,18b) having a space therebetween into which the teat (26) of the animal may be inserted. The membranes (18a,18b) are held by a support structure (12) under tension in a direction transverse to the direction of insertion of the teat (26), to protect the teat (26) from excessive force when the membranes (18a,18b) fall onto the teat (26).