A Monte Carlo method for the passage of electrons based on a single scattering model is developed. A code based on this method is operable on personal computers, and has been applied to analyze electron behavior in a layered system consisting of Ti (an accelerator window), air, cellulose triacetate (CTA) and backing material irradiated by 300 keV electrons. The energy spectra and the angular distributions of electrons on the CTA surface as well as depth distributions of energy deposition in the CTA for various backing materials have been obtained. Some of these results are compared with experiments, and show fairly good agreement.