Classical Coulomb cross sections, which make approximate allowance for binding of the atomic electrons, have been used for calculating electron slowing down spectra. The main result of binding is to increase the flux at low energy which improves agreement with experiment. Calculations were made for four specific cases of beta ray sources in aluminum, copper and gold for which experimental results are available. In a simplified, empirical version of the theory it was found that the calculations were in reasonable agreement with experiment down to about 300 eV for all three metals. However, attempts to improve the results by more detailed consideration of the electronic structure of the metals showed that the particular classical model on which these cross sections are based is not adequate.