Abstract: A continuous strip (3) of material advancing along a given feed direction (A) is shaped by a device (1) that comprises a rotating drum (6a), around which the strip (3) is looped at least in part, and a laser cutting head (7). The laser head (7) operates from the side of the strip (3) opposite to the drum (6a), which is furnished internally with a first pressurized chamber (10a) able to generate an extracting or blowing action on smoke produced by the laser cutting process, and a second chamber (10b) adjacent to the first, by which scrap material cut from the strip (3) is detached and retained on the drum. Smoke produced by the laser cut is distanced from the strip (3) almost instantaneously by a blower (14) located between the cutting head (7) and the drum (6a), and thus prevented from condensing and hardening on the cut edge of the strip (3).