A milking method susceptible of automation employs a teat cup with a support surface projecting to one side of the top of the cup. The cup is moved laterally against a teat until this lays on the support surface, after which movement is reversed while suction is applied to the cup, so that the teat falls and is sucked into the cup. A machine for carrying out the method can be controlled in response to signals from an electronic camera, touch or proximity sensors on the teat cup, and a vacuum sensor signalling entry of a teat into the cup.