This paper presents a model of inelastic electron scattering in a substance, taking into account surface effects. The surface effects were taken into account when calculating the differential cross sections of inelastic scattering based on the dielectric theory of Drude. In this paper, the transmission function was calculated when solving the transfer equation using two methods: the matrix method and the Monte Carlo method. Based on the transmission functions obtained, the energy spectra of X-ray photoelectron spectroscopy (XPS) were calculated. Computational and simulation models of inelastic electron scattering in matter have been proposed to implement methods for solving the transport equation.