Abstract: A machine for cutting sheet material by means of a laser beam comprises a table with an opening through which the laser beam passes and, situated under the table below the opening therein which is itself coaxial with the axis of the laser beam, a vessel containing a conical cap to deflect the rays of the laser beam with the object of dispersing the energy of the beam. This vessel contains an inclined grid which receives the work members cut out from the sheet, which members collect on the grid and can be periodically removed therefrom through an opening provided in the front wall of the vessel. A conduit for the evacuation of the residual cutting gas opens vertically below the cap. The waste (scoria, calamine) as well as the coolant or lubrication liquid passes through the grid and accumulates at the bottom of the lower part of the vessel. This liquid is evacuated through a pipe.