An apparatus for producing a web of fibrous material includes a roll having incisions with a depth of 0.01-2.00 mm, a width of 0.01-2.00 mm, and a pitch 0.01-10.00 mm, and rotated at a peripheral velocity v1 equal to the velocity of an upstream apparatus unit; a belt stretched between transmission rollers that advances at a velocity v2 less than v1, wherein v1/v2 lies between 1.05 and 1.40; a presser roller rotating at a peripheral velocity v2, associated with a presser system acting to press the belt against the metal roll with a pressure of 1-200 kg per centimeter; and a system that feeds a sheet of pliable fibrous material between the belt and the roll, the belt having a longitudinal elongation of no more than 5%, dimensional stability along its entire length, a thickness of 1-10 cm, and a hardness 24-70° Shore A.