In spite of the great efforts made by the scientific community, up to now there is no agreement about the rheoencephalography (REG) capability to reflect cerebral blood flow (CBF). Moreover, a standard procedure and the optimal electrode arrangement have not been established yet. In a previous study, we found, using a classical four-shell spherical model of the head and solving it by numerical methods that, theoretically, there could exist an electrode arrangement to register an REG II free of extracranial contribution. In this paper, we have studied the influence of scalp thickness on the intracranial contribution to REG II. The study has been performed by solving the head model, using in this case analytical methods, and then estimating the partial contribution of CBF pulsatility to REG for a given set of scalp thicknesses. Although our theoretical results validate the previous finding and suggest that, in some cases, an optimal electrode arrangement to register REG II exists, such an arrangement, and even its existence, is very sensitive to the subject's scalp thickness. According to this, there could not exist a universal electrode arrangement suitable for all individuals to register an REG II free of extracranial contribution, since it depends on the subject's physical constitution. This fact could explain the lack of agreement in the literature about REG interpretation.