We have been developing an active, non-destructive detection system based on nuclear resonance fluorescence (NRF) for inspecting special nuclear materials (SNMs) such as 235U in a container at a seaport. The study of the NRF yield dependence on the target thickness of SNMs is required to evaluate the performance of the inspection system. To this end, an NRF experiment has been performed using a laser Compton backscattering γ-ray beam line at New SUBARU in 208Pb. Cylindrical shaped natural lead targets with a 0.5 cm radius and varying thicknesses of 1.0, 1.44, and 3.05 cm were irradiated at a resonance energy of 7.332 MeV. The NRF yield was detected using two HPG detectors with relative efficiencies of 120% and 100% positioned at scattering angles of 90° and 130°, respectively, relative to the incident γ-ray beam. As a result, the NRF yield exhibited a saturation behavior for the thick lead target. An analytic treatment and Monte Carlo simulation using GEANT4 was performed to interpret the reaction yield (RY) of the NRF interaction. The simulation result is in good agreement with the experimental data for the target thickness dependence. The analytic treatment, the NRF RY model, is also in reasonable agreement.