An apparatus for processing a flexible material, comprising: - a first roller extending along a main axis; - a second roller extending along a longitudinal axis, the first roller and the second roller being mutually co-operating to carry out an operation on the flexible material, an interspace being defined between the first roller and the second roller so that the flexible material may pass through the interspace; - a pressing device for pushing the first roller and the second roller one towards another; - a position adjustment device for adjusting the relative position of the first roller and the second roller, the position adjustment device being distinct from the pressing device; - a pair of contact elements (17, 20) mounted at a front end respectively of the first roller and second roller, and a further pair of contact elements (27, 30) mounted at a rear end respectively of the first roller and second roller, the contact elements (17, 20) of said pair being arranged in mutual contact, and the contact elements (27,30) of said further pair being arranged in mutual contact, so as to define said interspace; - wherein the pressing device comprises at least two pressing elements which are arranged in contact with angularly spaced zones of a contact element (17, 20) of said pair, and at least two further pressing elements which are arranged in contact with angularly spaced zones of a contact element (27, 30) of said further pair; - characterised in that said pressing device comprises a pair of pneumatic cylinders to which corresponding pivoting rocker arms are connected, each rocker arm being connected to a pair of support elements (54, 64) in a tiltable manner, the support elements (54, 64) supporting said pressing elements or respectively said further pressing elements. - a first roller extending along a main axis; - a second roller extending along a longitudinal axis, the first roller and the second roller being mutually co-operating to carry out an operation on the flexible material, an interspace being defined between the first roller and the second roller so that the flexible material may pass through the interspace; - a pressing device for pushing the first roller and the second roller one towards another; - a position adjustment device for adjusting the relative position of the first roller and the second roller, the position adjustment device being distinct from the pressing device; - a pair of contact elements (17, 20) mounted at a front end respectively of the first roller and second roller, and a further pair of contact elements (27, 30) mounted at a rear end respectively of the first roller and second roller, the contact elements (17, 20) of said pair being arranged in mutual contact, and the contact elements (27,30) of said further pair being arranged in mutual contact, so as to define said interspace; - wherein the pressing device comprises at least two pressing elements which are arranged in contact with angularly spaced zones of a contact element (17, 20) of said pair, and at least two further pressing elements which are arranged in contact with angularly spaced zones of a contact element (27, 30) of said further pair; - characterised in that said pressing device comprises a pair of pneumatic cylinders to which corresponding pivoting rocker arms are connected, each rocker arm being connected to a pair of support elements (54, 64) in a tiltable manner, the support elements (54, 64) supporting said pressing elements or respectively said further pressing elements.