The dependence of the nuclear resonance fluorescence (NRF) yield on the target thickness was studied. To this end, an NRF experiment was performed on 238U using a laser Compton back-scattering (LCS) γ-ray beam at the High Intensity γ-ray Source facility at Duke University. Various thicknesses of depleted uranium targets were irradiated by an LCS γ-ray beam with an incident beam energy of ∼2.475 MeV. The scattering NRF γ-rays were measured using an High-purity Germanium (HPGe) detector array positioned at scattering angles of 90° relative to the incident γ-beam. An analytical model for the NRF reaction yield (NRF RY model) is introduced to interpret the experimental data. Additionally, a Monte Carlo simulation using GEANT4 was performed to simulate the NRF interaction for a wide range of target thicknesses of the 238U. The measured NRF yield shows the saturation behavior. The results of both of the simulation and the analytical model can reproduce the saturation curve of the scattering NRF yield of 238U against the target thickness. In addition, we propose a method to deduce the precise integral cross section of the NRF reaction by fitting the NRF yield dependency on the target thickness without any absolute measurements.