Abstract: Apparatus for removing break-out portions and in particular waste pieces from a sheet of material which contains blanks or the like and which rests on a break-out surface in such a way that the break-out portion extends over an aperture in the break-out surface and is pressed downwardly through the aperture under the pressure of at least one break-out member, in particular a break-out pin. Associated with the break-out member beneath the break-out portion is a support which is guided in the direction of movement of the break-out member. The support is a surface which is springy and/or movable within the aperture at least partially into a position at a spacing relative to the break-out surface and which in its rest position engages beneath the waste piece in the sheet of material and which is adapted to be transferred into an inclined position relative to the sheet of material upon movement of the waste piece by the break-out member, in particular upon downward movement of the waste piece.