The apparatus for separating residues from a thermal waste treatment into one fine fraction and one coarse fraction comprises a housing (1) abutting on swinging elements (2), said housing having a plurality of diagonally offset plates (3.1-3.5) that are disposed one beneath the other and are connected to said housing (1) by their side edges, and being equipped with means (5) for generating a vibration component oriented in the direction of the plates (3.1-3.5) disposed diagonally offset downward.The apparatus further comprises one suction line (6) as well as an inlet opening for a gas that may be passed between the plates for wind sieving. Residues or slag from a waste treatment plant or an incineration plant are supplied to this apparatus in order to separate them into at least one fine fraction and one coarse fraction.