The scattered photon flux of primary photons in the energy ranges from 640 to 680 keV, from 340 to 360 keV, and from 200 to 220 keV was calculated by Monte Carlo methods. The results were computed for cylindrical geometry. A semi-empirical formula was fitted to the calculated values. To expand the usefulness of the response functions obtained, a composition characterization parameter ɸ was defined and used. A method for analyzing the errors associated with multiple gauging of composition and density has been developed. It is shown that a gamma-ray gauging technique using primary transmitted photons in conjunction with a scattered component represents a very powerful combination of assay methods.