A method for draining the tank space (20) of a supply tank or feed chute in a pneumatic material conveying system, such as a waste conveying system, of material, such as waste material, in which method the tank space (20) is drained to a conveyor pipe (3) by opening an outlet valve (4), so that the underpressure prevailing in the conveyor pipe, together with the ambient pressure prevailing in the supply tank transfers material from the supply tank to the conveyor pipe (3). In the method, in the supply tank, a wall element (6) positioned at a distance from the outlet aperture (8) of the supply tank and / or from the outlet valve (4), which wall element (6) is arranged to move between at least two positions, i.e. a first position, where the wall element (6) restricts the access of material to the vicinity of the supply tank outlet aperture (8), and a second position, where the wall element (6) does not essentially restrict the access of material to the vicinity of the supply tank outlet aperture (8), is shifted from the first position to the second position. The invention also relates to an arrangement.