A continuously conveyed tubular plastic foil is perforated by a laser beam which is focused by a mirror or lens on the perforation forming plane, lying at the focal point of the mirror or lens, of a tautly conveyed tubular plastic foil. For taut conveyance of the tubular foil it is guided over a support placed in the tubular foil, or over supporting plates, lying outside the tubular foil and provided with a foil suction device and with laser beam transmission apertures. The slightly tapering perforations with a minimum aperture at the inside of the tubular foil form, on the one hand, a pattern of parallel lines running in the lengthwise direction and, on the other hand, a pattern of parallel lines which run at an angle relative to the longitudinal axis of the flattened tubular foil. A bag can be formed from the tubular foil. An apparatus for perforation is made up of, in addition to a laser beam source, a lens beam-directing device and a lens or mirror, a support to be placed in a tubular foil, or supporting plates, provided with apertures and with foil suction apertures, for taut conveyance of the tubular foil in a perforation forming plane.