Device for severing components made from brittle material, for example, glass, ceramics, glass ceramics, by producing a thermally-induced stress fracture on component in a separation zone includes a laser for directing a laser beam onto component to be machined so that component partly transmits laser beam with partial absorption at least twice simultaneously or serially along separation zone at the same point or closely spaced points. Device includes a bearing surface on which component being machined is received, and device for subjecting component to mechanical stresses for promoting thermally induced stress fracture. Bearing surface has at least two bearing surface sections movable relative to each other between a first position and a second position, and component, in the first position, being supported in a manner substantially free from mechanical stresses, and, in a second position, component being subjected to mechanical stresses for promoting the thermally induced stress fracture.