Reflected Global Positioning System (GPS) signals can be used to infer information about soil moisture in the vicinity of the GPS antenna. Interference of direct and reflected signals causes the composite signal, observed using signal-to-noise ratio (SNR) data, to undulate with time while the GPS satellite ascends or descends at relatively low elevation angles. The soil moisture change affects both the phase of the SNR modulation pattern and its magnitude. In order to more thoroughly understand the mechanism of how the soil moisture change leads to a change in the SNR modulation, we built an electrodynamic model of GPS direct and reflected signal interference, i.e., multipath, that has a bare-soil model as the input and the total GPS received power as the output. This model treats soil as a continuously stratified medium with a specific composition of material ingredients having complex dielectric permittivity according to well-known mixing models. The critical part of this electrodynamic model is a numerical algorithm that allows us to calculate polarization-dependent reflection coefficients of such media with various profiles of dielectric permittivity dictated by the soil type and moisture. In this paper, we demonstrate how this model can reproduce and explain the main features of experimental multipath modulation patterns such as changes in phase and amplitude. We also discuss the interplay between true penetration depth and effective reflector depth. Based on these modeling comparisons, we formulate recommendations to improve the performance of bare soil moisture retrievals from the data obtained using GPS multipath modulation.