This paper presents the results of Monte Carlo modelling of the sensitivity of the lithium containing detectors CLYC, NaIL, CLLB to thermal neutrons. The difference between the sensitivity and the neutron freepath depth of the CLYC scintillator enriched and unenriched with the 6Li isotope is shown. The analysis of the distribution of alpha particles and neutrons in the scintillator volume is performed, showing the inefficiency of the unenriched scintillator due to the fact that not all neutrons react with the crystal material. Mathematical modelling by the Monte Carlo method of the scintillator sensitivity and its comparison with respect to the irradiation direction has been carried out. It is shown that for the scintillator in the face and side geometry with the size more than 38 mm the difference in sensitivity at change of the neutron flux direction is connected only with the scintillator cross section and 6Li concentration with the same value of the specific sensitivity. The obtained model results were compared with available experimental data for NaIL and CLLB scintillators, which showed the reliability of the developed models and calculation methods.