paper that comes in a roll rather than in sheets. A web press runs this paper, folding and/or cutting it after it is printed. web press a press specifically designed to print rolls of paper called webs, rather than sheets. A web press runs much faster than a sheet fed press: as many as 40,000 images per hour versus a maxi- mum of about 14,000 per hour on a sheet fed press. see also offset, sheet-fed press, web, web paper.