The interaction of a focused beam of monochromatic electrons with a solid sample is a complex many-particle problem, which cannot be fully described by analytical methods. But already in the early sixties trajectories of single electrons were simulated numerically on computers (1,2,3). This method was called Monte Carlo simulation (MC). Sequential simulation of some thousand trajectories accumulates a set of data, sufficient to provide information about -fraction of backscattered electrons,-fraction of transmitted electrons in case of thin film samples,-ionization probability for certain electron shells as a function of sample depth,-calculation of x-ray intensities generated in or emitted from the sample,-energy distribution of backscattered electrons or of electrons in certain depth,-calculation of signal generation in samples with complex geometries. For all these applications the physical processes of electron - solid interaction needed to be described as realistic and accurate as possible, which was always - and is still - in contradiction to the limitations of existing theories, their applicability in such a complex problem, and of course to the limitations of computer capacities.