An X-ray apparatus provides rotationally symmetric, Gaussian-like focal spot distributions. The apparatus may be constituted by an X-ray tube having a glass envelope, a cathode in the form of a filament for providing thermionically emitted electrons and an anode. The anode is of conical shape and can be rotated. The cathode is arranged to be rotated about an axis perpendicular to the plane of the filament and passing through its central point. The apparatus may be constituted by a conventional X-ray tube which is rotatable about an axis coaxial with the central ray of the X-ray field which emerges from the tube. The apparatus may be constituted by a conventional X-ray tube, which is stationary, in combination with a mechanism which effects rotation of the X-ray image receptor and the object being to be examined about an axis coaxial with the central ray of the X-ray field.