Process for removing peripheral portions such as bead regions of a glass sheet including a step of pushing the glass sheet in the peripheral portion using a pushing mechanism such as a pushing bar, and corresponding apparatus. As a result of the use of the pushing mechanism, the engagement completion time for suction cups, if used, are reduced significantly. A process without using suction cups is enabled with enhanced yield. The increased process stability and enlarged process window are particularly advantageous for processing glass sheets having high flexibility.