Abstract: An X-ray fluorescence spectrometer comprising an X-ray source, a sample holder spaced from the X-ray source at a distance which ensures the illumination of the central portion of the sample not less than 0.3 ZU erg./s.cm.sup.2.w, where Z is the atomic weight of material of the X-ray anode and U is the voltage across the X-ray source, in kilovolts. The spectrometer further comprises a curved analyzing cristal for focusing the fluorescent radiation of the sample at an X-ray detector. The analyzing cristal and the detector are installed in an evacuated chamber. The X-ray source and the sample holder are positioned outside the evacuated chamber which has a window for passing X-ray radiation. The sample holder is positioned so that the average distance between the sample surface portion which produces radiation incident on the analyzing cristal and the window does not exceed the distance between said sample surface portion and the focus of the X-ray source.