An apparatus for the inspection of the heat shield of a space shuttle has a drive so that it can automatically undertake an examination of the tiles of the heat shield. The apparatus moves over the surface with the aid of the drive, and images of the region to be inspected are produced with the aid of a camera. For these images, the tiles are illuminated subsequently by light sources from different directions, as a result of which the tiles can be reliably evaluated with regard to possible defects.