Monte Carlo method is one of the approaches to determine the efficiency of a detector. In this thesis, the dependence of intrinsic efficiency on NaI(Tl) and CsI(Tl) inorganic cylindrical scintillation detectors on source-detector distance (h), source off-axis distance (?) and gamma photon energy (E) have been investigated using analytical and Monte Carlo methods. The detector geometry was defined as a cylinder with a length and diameter (2R) of 3 inches. An isotropic point source was placed at a distance of h from the detector window. This source can be located either on the cylinder axis (on-axis mode) or at the distance ? from the cylinder axis (off-axis mode). Firstly, the intrinsic efficiencies of NaI(Tl) and CsI(Tl) cylindrical detectors were analytically calculated for different energies. Then, the intrinsic efficiency was computed for 1.5 MeV gamma photons and various distances between the source and detector at both on-axis (? = 0) and off-axis (? = 1.5, 2.5, 3 cm) modes by the MCNP code for NaI(Tl) cylindrical detector. The efficiency values obtained through the MCNP code were compared with analytical results for 1.5 MeV gamma photons. To achieve more certainty, the intrinsic efficiency was calculated at on-axis mode for energies of 0.2, 1 and 5 MeV and off-axis mode for a 0.662 MeV energy. The obtained results were compared to other published data. Intrinsic efficiency calculation of NaI(Tl) detector at on-axis mode for 0.2, 1, 5, 10 and 50 MeV as well as at the off-axis mode for 0.662, 1.5 and 2.75 MeV have been calculated in previous research works. In addition to those previous data, in this thesis, the intrinsic efficiency (? in ) of NaI(Tl) was calculated for the off-axis mode at 0.2, 1, 5, 10 and 50 MeV to validate the implemented code. Also, ? in versus h/R is plotted for obtained results. Next, the intrinsic efficiency of CsI(Tl) was calculated at the on-axis mode for 0.2, 1 and 5 MeV, and the results were compared to other reported results. Likewise, the intrinsic efficiency of CsI(Tl) was computed at the off-axis mode for E=0.2, 0.662,1, 1.5, 2.75, 5, 10, and 50 MeV by the MCNP code as well as an analytical method. Thus, to verify the code programmed for CsI(Tl) these two methods have been compared. Then, ? in versus h/R is plotted for CsI(Tl) detector at on-axis and off-axis modes for energies of 0.2, 0.662, 1, 1.5, 2.75, 5, 10 and 50 MeV. Finally, the plotted data for NaI(Tl) and CsI(Tl) were analyzed and discussed.