A method for producing a breathable web (W), comprising: - feeding a web (W) on the surface of an anvil roller (16) rotatable about its axis (A) and having a plurality of welding protrusions (20) cooperating with a welding element (18), - welding said web (W) at a plurality of welding spots (44) on head surfaces (22) of said welding protrusions (20) and forming respective annular welding seams (46) at said welding spots (44), about respective welding projections (20), and respective thin membranes (48) located within said annular welding seams (46) and adjacent to the head surfaces (22) of said welding protrusions (20), and - removing said thin membranes (48) after said welding by means of a peeling roller (36) having an outer surface tangent to said head surfaces (22) of said welding protrusions (20).
