A method for making laser engravings on a web made of a paper material, a natural or artificial polymeric material or a metal material, said method comprising the steps of: - prearranging a web conveying means configured for conveying a web in a predetermined direction; - defining a working area along a path of said web; - prearranging a laser pulse emitter for emitting laser pulses (15,15',16) that have a power set to form engravings on said web; - prearranging a movable pointing means (22,23,33) that comprises a reflection means (22,23) and a focus means, said movable pointing means configured for sending said laser pulses (15,15',16) into said working area; - selecting an engraving pattern, comprising a plurality of points to be engraved on said web by said laser pulses (15,15',16) emitted as pulse packets in quick succession, said pattern associated with a first function that defines the position of said points in said working area with respect to a first reference system that is integral to said web; - calculating an instruction file containing pointing instructions for operating said pointing means (22,23,33) in such a way that a predetermined position of said movable pointing means (22,23,33) corresponds to each pulse packet, a predetermined position of said points on said working area corresponding to said predetermined position of the movable pointing means; - selecting an emission power of said laser pulse emitter; - emitting laser pulses at said emission power through said emitter; - operating said movable pointing means (22,23,33) according to said instruction file, so that said movable pointing means (22,23,33) sequentially reaches each predetermined position by continuously changing the direction of said laser pulses (15,16) in said working area reproducing said pattern on said web; characterized in that said step of calculating an instruction file provides a transform of said first function from said reference system that is integral to said web, into a second reference system that is integral to said emitter, wherein a second transformed function is obtained, by said transform, which is defined in said working area, and in that said instructions of said instruction file operate said pointing means (22,23,33) in such a way that said laser pulses describe said transformed function with respect to said second reference system, in said working area, such that said packets of laser pulses reach said web, and engrave said pattern on said web as if said web were motionless. - prearranging a web conveying means configured for conveying a web in a predetermined direction; - defining a working area along a path of said web; - prearranging a laser pulse emitter for emitting laser pulses (15,15',16) that have a power set to form engravings on said web; - prearranging a movable pointing means (22,23,33) that comprises a reflection means (22,23) and a focus means, said movable pointing means configured for sending said laser pulses (15,15',16) into said working area; - selecting an engraving pattern, comprising a plurality of points to be engraved on said web by said laser pulses (15,15',16) emitted as pulse packets in quick succession, said pattern associated with a first function that defines the position of said points in said working area with respect to a first reference system that is integral to said web; - calculating an instruction file containing pointing instructions for operating said pointing means (22,23,33) in such a way that a predetermined position of said movable pointing means (22,23,33) corresponds to each pulse packet, a predetermined position of said points on said working area corresponding to said predetermined position of the movable pointing means; - selecting an emission power of said laser pulse emitter; - emitting laser pulses at said emission power through said emitter; - operating said movable pointing means (22,23,33) according to said instruction file, so that said movable pointing means (22,23,33) sequentially reaches each predetermined position by continuously changing the direction of said laser pulses (15,16) in said working area reproducing said pattern on said web;