In this article, the authors propose a new technique for measuring linear attenuation coefficients on the medical linear accelerator Elekta Axesse. Linear attenuation coefficients were obtained for four samples at different concentrations of substances at a gamma-ray energy of 6 MeV. A unified ionization chamber was used as a detector to register the transmitted gamma-ray beam through the samples under study. Linear absorption coefficients were obtained for elements B, C, O, S, Fe, Ba taking into account their concentration, as well as taking into account the different mass inclusion of paraffin in the samples under study, which is acyclic hydrocarbons CnH2n+2. The measurement results showed that taking into account certain components in impurities leads to relatively small, but quite noticeable differences in the determination of the total absorption coefficients. This is especially important to take into account for determining the concentration of light elements in samples. To determine the content of medium and heavy chemical elements, taking into account the content of light elements can be neglected. The use of a 6 MeV gamma-ray beam made it possible to reduce the errors in determining the absorption coefficients, since their dependence on energy in the region of applicable gamma-ray energies is not so great in comparison with the low-energy region, in which the shell effects for heavy elements will introduce significant contribution.