A milking device includes a vessel and cover plate. The vessel and the cover plate form a sealed volume that is internally divided into a collecting chamber, a vacuum chamber and an air intake chamber. The collecting chamber is arranged between the vacuum chamber and the air intake chamber. The vessel has a first internal wall that separates the collecting chamber from the air intake chamber, with a first passage between the collecting chamber and the air intake chamber arranged at the first internal wall. The vessel has a second internal wall that separates the collecting chamber from the vacuum chamber, with a second passage between the collecting chamber and the vacuum chamber arranged at the second internal wall.