A description is given of a Monte Carlo method for the computation of electron trajectories in solids. The calculations are based on the Bethe energy loss law and the Rutherford scattering equation. By assembling a large number of these trajectories, predictions are made on the transmission, backscattering, angular distribution and energy spectrum of electrons passing through thin films. The results are in good agreement with experimental data on the passage of electrons, initially of energy from 5 to 30 keV, through aluminium, aluminium oxide, copper and gold.