A method for draining the tank space (20) of a supply tank (1) in a pneumatic material conveying system, such as a waste conveying system, from material (10), such as waste material, said conveying system comprising at least one feed point of material, particularly waste material, such as a supply tank (1); said tank comprising a tank space (20); in which method the tank space is drained to a conveyor pipe (2, 100) by opening a drain valve (3), so that the underpressure prevailing in the conveyor pipe, together with the ambient pressure prevailing in the supply tank, conveys material from the supply tank to the conveyor pipe (2, 100). In the method, makeup air is brought to the vicinity of the outlet aperture (8) of the supply tank (1), and the material (10) is guided by a partition wall element (9) towards the outlet aperture, so that the makeup air affects the material to be discharged (10) in the vicinity of the outlet aperture (8), at least during the draining step. The invention also relates to an arrangement.