Abstract Monte Carlo transport methods are used to simulate the scattering of X-rays in polystyrene and iron slabs. The calculations are made with monoenergetic X-ray sources in the energy region from 30 keV (100 keV for iron) to 20 MeV. This energy range includes the energy regions for diagnostic radiology (0.03–0.15 MeV), nuclear medicine (0.1–2.0 MeV) and industrial radiography (0.2–20 MeV). slab thicknesses for polystyrene were 53, 100, and 210 mm and for iron 7 and 14 mm. The present calculations include the effects of secondary electron/positron radiation which become quite important at high energies. As a function of the incident photon energy, the ratio of the scattered to the total radiation (scatter fraction) was found to have a characteristic ‘N’ shape. Increasing the atomic number of the scattering media has the effect of ‘squeezing the N’.