An investigation of the effects of plural elastic scattering events on the intensity-angular distributions of electrons scattered in thin films has been carried out using single scattering functions based on the free-atom formulation in the first and second Born approximations. Thin films of elements were chosen which were representative of a variation of proton number across the periodic table: carbon (Z=6), germanium (Z=32) and gold (Z=79).The results show that at high incident electron energy (100 keV) the difference in the intensity-angular distributions calculated from single scattering functions in the first and second Born approximations increases with increasing proton number, with correspondingly larger differences for thicker films. The differences for carbon, however, were negligible. At low incident electron energy (10 keV) the above behaviour was much more exaggerated, and in the case of carbon the differences were significant.