In a low-deformation support device of an optical element (8, 24), in particular an end plate (14) of a projection objective (7) of a projection exposure machine (3) for microlithography for the purpose of producing semiconductor components, in a mount (13), the optical element (8, 14) is connected to the mount (13) at least partly via a bonded connection. The bonded connection is located between the adjacent circumferential wails of mount (13) and optical element (14). The mount (13) is provided with at least three bearing elements (20) which are distributed over the circumference and by means of which the optical element (8, 14) is laterally and axially supported. The mount (13) has spring elements (15) which are constructed monolithically with the bearing elements (20) and are soft in axial and radial directions.