A rotary parlour for milking of animals includes an annular rotary platform (20) adapted to form a support surface (18) for the animals (22), positioning elements (19, 23) for arranging the animals (1) in milking positions on the platform (20), a drive mechanism (30) adapted to supply a rotational motion to the platform (20), and teat cup storing devices (11) for holding parked teat cups (2, 2') in predetermined storing positions. The teat cup storing devices (11) are mounted in positions such that the teat cups (2, 2') are located vertically above the platform (20) in their storing positions.