From one aspect the invention is a method of classifying waste materials comprising arranging two sieve screens, each having an inlet end and an outlet end, one above the other to define a space there between, arranging the upper screen, to be of coarser mesh size than the lower screen, supplying waste material to be classified to the inlet end of the upper screen, vibrating the screens, and blowing air between the screens from the inlet end and towards the outlet end whereby the waste material being blown away from the outlet ends of the screens, and large heavy material falling under gravity from the outlet end of the upper screen, and separately collecting the separated waste material fractions. From another aspect the invention is an apparatus for carrying out the method described above.