A computational procedure is proposed to perform uncertainty analysis for the calculation of the isotopic inventory and radiological quantities obtained as a linear function of it, due to uncertainties in the activation cross sections. The method is applied to determine the uncertainty of the calculated shallow burial index (SBI) from activated type 304 stainless steel (SS) in the most neutron-exposed zone of the HYLIFE-II vessel structure. Results are obtained by means of an element-by-element study. Some other types of steel are also investigated for comparison purposes. The SS304 is confirmed to be the most promising steel option.