[en] Since years irradiations of HTR-spherical fuel elements have been done, in the course of which the target burnup of the nuclear fuel has a fixed value. For the prediction of the shutdown moment it is necessary to know the momentary fuel burnup state of the irradiation experiment at any time. On account of the construction of the irradiation rig the fuel burn up determination can only be performed by calculation. Only after the irradiation end, the reached fuel burnup can likewise be measured by γ-spectrometry or by mass spectrometry. The report describes the neutronic calculations which are needed for the fuel burnup determination. Under the given circumstances especially the selfshielding correction for the spherical fuel element is accentuated which in the case of low enriched fuel is inevitable because of the resonance absorption of the neutrons in the nuclear fuel U238. It appears, that under optimal circumstances our burnup calculation is feasible with an average relative single standard deviation of approximately 7%. In the case of the irradiation experiment JK13 there was found an agreement between the total burnup which was calculated by our treatment on one hand, and those which was measured in the hot cells of the KFA on the other. This statement refers to a statistical significance level of 95%. (orig./HP)