The objective of this work is to present a method/technique for the determination of the effective atomic number (Zeff) of composite materials [mixed materials of many atomic numbers (Z's)]. In the present measurements, an intense beam of gamma-ray photons irradiates targets of different elements and composite materials and of varying thicknesses. The scattered radiations are detected by a properly shielded NaI(Tl) scintillation detector whose response unfolding, converting the observed pulse-height distribution to a true photon spectrum, is obtained with the help of an inverse matrix approach. This also results in the extraction of the numbers of multiple-scattered events from the thick targets. We observe that the numbers of multiple-scattered events, having the same energy as in single-scattered distribution, increase with an increase in target thickness and then saturate for a particular target thickness known as saturation thickness (depth). The saturation thickness is found to decrease when the Z of pure elements increases. A calibration curve (saturation depth versus Z of pure elements) and the measured saturation thickness values for composite materials are used to assign the respective Zeff values of these composite materials. Monte Carlo calculations also support the present experimental results.