A device for perforating cigarette wrapping material by means of at least one-laser beam, whereby the wrapping material, in the form of a strip, is fed past a focusing head which is supplied with a pulsed laser beam by a laser source and focuses it on to the strip by moving the focused beam in a plane slanting in relation to the traveling direction of the strip; a shutter element, made of material impervious to the laser beam, being used for intercepting and restricting the focused beam to a sector of given shape and size, and so preventing the beam from impinging on given portions of the strip.