A mathematical model of the output signals of an X-ray sandwich detector is presented. Based on this model, two mathematical models of the radiation transparency of the test object for a sandwich radiation detector have been developed. These models are the basis for a theoretical assessment of the accuracy of recognizing materials using the corresponding implementation scheme of the dual-energy method. The fundamental difference between the developed models is that one of them does and the other does not take into account statistical dependence between the output signals of the sandwich detector. Recommendations on the preference for using each of these models are given.