The method includes the stages of gluing of a plurality of layers of sheet material (2, 3, 4); and stamping of all the layers (2, 3, 4) together; with sticking together of the previously glued zones being carried out at the same time as the stamping of all the layers (2, 3, 4). The machine includes gluing stations (12); and a stamping station (13) which includes a pair of pressing elements, which stamp and stick together said previously glued layers. The laminar element is formed from a plurality of layers of sheet material (2, 3, 4) and can include one or several cavities (5) of polygonal profile, or else said layers are of sinusoidal profile. A higher manufacturing output of the laminar layer is achieved and it permits the forming of a laminar element with cavities or undulations of any desired shape, without limitation on the thickness of the layers.