Abstract: Method of mechanically milking a lactating animal, such as a cow, a goat and a sheep, comprising: providing an animal having at least one teat (110), said teat comprising an elongate shaft (112) and a teat end (114) at an end of said shaft, said teat end comprising a teat canal (116) having an external orifice (118); milking the teat (110) by repeatedly alternatingly increasing and decreasing a diameter (D) of at least a longitudinal portion of its shaft (112), while maintaining a substantially axi-symmetric shape of said portion of the shaft, and while continuously applying a milking vacuum to the teat end (114) so as to extract milk from the external orifice (118) of the teat canal (116). Also disclosed is a teat cup liner for practicing the disclosed method.