A machine for processing flat printing material, in particular a sheet processing rotary printing press, includes at least one processing station in the form of a printing unit, a feeder for loading the processing station with sheets of the printing material, a delivery for combining the processed sheets into piles, and an auxiliary pile carrier displaceable in an insertion direction from a standby position into an operational position and vice versa. Supporting members follow one another in the insertion direction and axially parallel swivel joints articulatingly connect the supporting members directly to one another. The supporting members have extensions projecting beyond the swivel joints thereof. One of the extensions directed counter to the insertion direction of a respective one of the supporting members engages underneath one of the extensions directed in the insertion direction of the respective supporting member after the next which trails in the insertion direction.