A process for making a continuous web of a longitudinally corrugated fibrous material includes passing the web between a rigid cylinder having circumferential grooves that are flanked and shaped to define a substantially corrugated profile on substantially on the entire thickness of the web, and a presser which has an external layer made of an elastically compressible material and which is maintained adherent to the rigid cylinder so as to cause the continuous web to penetrate into the grooves and thus obtain the corrugations, At the same time, the continuous web is subjected to a reduction of the speed of the surface in contact with the presser with respect to the speed of the surface in contact with the rigid cylinder so as to have a longitudinally corrugated pattern on both surfaces and transverse ripples at least at the corrugated surface that was in contact with the rigid cylinder.

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