Abstract: A method and apparatus for laser cutting sheet material and especially for laser cutting composite sheet material. An inert gas shield, preferably of nitrogen, is provided at the cutting zone to minimize charred edges of the cut material and resulting in an extremely accurate and uniform cut line. The gas shield can also be used to accurately position the sheet material so as to lie at the focal point of the laser beam. Alternatively, a vacuum can draw the sheet material against a supporting surface for positioning the sheet material. In a continuous process, one or more stationary lasers operating on an advancing web of the sheet material are positioned to cut in the longitudinal direction and a movable laser is positioned to cut in the transverse direction. Mechanical expedients enable the movable laser to make a cut perpendicular to the cut made by each stationary laser without interrupting the flow of the sheet material.