The dosimetry of internal exposure to radionuclides is performed on the basis of biokinetic and dosimetric models. For prospective purpose, the organ or effective dose resulting from potential conditions of exposure can be calculated by applying these models with dedicated software. However, it is acknowledged that a significant uncertainty is associated with such calculation due to the variability of individual cases and to the possible lack of knowledge about some factors influencing the dosimetry. This uncertainty has been studied in a range of situations by modeling the uncertainty on the model parameters by probability distributions and propagating this uncertainty onto the dose result by Monte Carlo calculation. However, while probability distributions are well adapted to model the known variability of a parameter, they may lead to an unrealistically low estimate of the uncertainty due to a lack of knowledge about some input parameters. Here we present a mathematical method, based on the Dempster-Shafer theory, to deal with such imprecise knowledge. We apply this method to the prospective dosimetry of inhaled uranium dust in the nuclear fuel cycle when its physico-chemical properties are not precisely known. The results show an increased estimation of the range of uncertainty as compared to the application of a probabilistic method. This Dempster-Shafer method may valuably be applied in future prospective dosimetry of internal exposure in order to more realistically estimate the uncertainty resulting from an imprecise knowledge of the parameters of the dose calculation.