In the method for cutting a material layer (20) along a given cutting line (21), a cutting beam is moved so as to impinge on the material layer (20) laterally offset by a distance (W) from the cutting line (21). The distance (W) is determined as a function of the variations of the cutting speed at which the cutting beam is moved, and/or as a function of the deviations of the effective cutting beam cross-section from a circular shape.