Electron scattering in thin solid films used for the fabrication of masks for electron projection lithography, e.g., SCALPEL(R), is investigated. We have developed an analytical model to calculate electron transmission through the mask membrane and image contrast due to different scattering properties of the patterned area and the membrane. The model utilizes cross sections for electron elastic and inelastic scattering on an atom with exponentially screened Coulomb potential of the nucleus derived in the first Born approximation. The variety and controversy of theoretical and empirical adjustments of the screening parameter are briefly analyzed and attributed to the misinterpretation of experimental data ignoring the effects mostly, due to plural scattering of electrons and dense packing of atoms in thin solid films. This model frees us from the computational limitations of Monte Carlo simulations and proves to be effective for the straightforward characterization of various alternative materials for SCALPEL mask membrane and scatterer. The model includes the appropriate effects of the projection optics and back-focal plane aperture.