Abstract: A laminating machine has an upper platen which is laterally rigid but transversely flexible. The upper platen is adjacent to a lower platen. Two sheets of material to be laminated together to form a laminated structure, such as a membrane switch, are held respectively on the upper and lower platens. A press roller is mounted behind the upper platen. The press roller is connected to an actuator that can sweep the press roller across the back face of the upper platen. The laminating cycle includes moving the upper platen so that it makes a shallow angle with the lower platen and advancing the press roller to flex the lower platen. The press roller is then advanced to compress the upper platen against the lower platen along a narrow nip which sweeps across the face of the lower platen. The machine avoids entrapment of air between the sheets which is a problem in prior laminating machines.