A rotary parlour for milking of animals, wherein the parlour comprises an annular rotary platform (20) adapted to form a support surface (18) for the animals (22), 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 and wherein 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. The rotary parlour comprises positioning means (19) adapted to arrange the animals in milking positions such that a longitudinal axis (22c) of the animals forms an angle of 20° to 80°, preferably 30° to 60°, to the direction of motion of the animal (22d) on the platform (20). The teat cup storing devices (11) are arranged in positions such that the teat cups (2), which are to be attached to an animal standing in a milking position, are located in a storing position on one side of said animal (22) and behind an animal (22) standing in an adjacent milking position.
