Multiple Compton scattering results in an incorrect evaluation of Compton profile, which usually examines the case when the photon has undergone only one Compton collision in the sample. The probability of a photon being scattered several times may be significant for a target of finite dimensions both in depth and lateral dimensions. The present measurements are carried out to study the energy and intensity distributions of 0.279, 0.662, and 1.12 MeV γ rays multiply scattered from the copper target of various thicknesses at a scattering angle of 60°. The scattered photons are detected by a NaI(Tl) scintillation detector whose detector response unfolding, converting the pulse-height distribution to a photon energy spectrum, is obtained with the help of an inverse response matrix. We observe that with an increase in target thickness, the number of multiply scattered photons saturates at a particular value of the target thickness (saturation depth). The multiply scattered fraction starts saturating above a particular energy window around the centroid of inelastic scattered peak. The signal-to-noise ratio is found to be decreasing with an increase in target thickness. Monte Carlo calculations based upon the package developed by Bauer and Pattison [Comptom Scattering Experiments at the HMI (1981), HMI-B 364, pp. 1-106] support the present experimental results. Copyright © 2006 American Physical Society.