EUV lithography is considered as a possible technology for the mass production of devices at the 32 nm technology node and beyond. One special characteristic of EUV masks is its composition (Mo/Si multilayer, absorbing layer, etc.) which is totally different for the conventional photomask. This has to be considered explicitly in the simulation of electron-beam energy dissipation calculation (EDF(r)) using Monte Carlo methods. So far the application of analytical methods is very difficult in the case of substrates more complex than resist/layer, 1/layer, 2/bulk layer. The Monte Carlo procedure is utilized for the electron-beam energy deposition in a resist film covering a multi-layer of Mo/Si layers on top of a Si substrate. The effect of the number of layers of the Mo/Si structure and their thickness in terms of incident electron energy, on the backscattering coefficient and on the deposited energy in the multilayer stack is investigated.