Background. Extensive studies have been conducted to simulate blood flow in the human vasculature using nonlinear equations of pulsatile flow in collapsible tube plus a network of vessels to represent the whole vasculature and the cerebral circulation. For non-linear models numerical solutions are obtained for the fluid flow equations. Methods. Equations of fluid motion in collapsible tubes were developed in the presence of gravitational force (Gforce). The Lax-Wendroff and MacCormack methods were used to solve the governing equations and compared both in terms of accuracy, convergence, and computer processing (CPU) time. A modified vasculature of the whole body and the cerebral circulation was developed to obtain a realistic simulation of blood flow under different conditions. The whole body vasculature was used to validate the simulation in terms of input impedance and wave transmission. The cerebral vasculature was used to simulate conditions such as presence of G-force, blockage of Internal Carotid Artery (ICA), and the effects on cerebral blood flow of changes in mean and pulse pressure. Results. The simulation results for zero G-force were in very good agreement with published experimental data as was the simulation of cerebral blood flow. Both numerical methods for solutions of governing equations gave similar results for blood flow simulations but differed in calculation performance and stability depending on levels of G-force. Simulation results for uniform and sinusoidal G-force are also in good agreement with published experimental results, Blood flow was simulated in the presence of a single (left) carotid artery obstruction with varying morphological structures of the Circle of Willis (CoW). This simulation showed significant differences in contralateral blood flow in the presence or absence of communicating arteries in the CoW. It also was able to simulate the decreases in blood flow in the cerebral circulation compartment corresponding to the visual cortex in the presence of G-force. This is consistent with the known loss of vision under increased acceleration. Conclusions. This study has shown that under conditions of gravitational forces physiological changes in blood flow in the systemic and cerebral vasculature can be simulated realistically by solving the one-dimentional fluid flow equations and non-linear vascular properties numerically. The simulation was able to predict changes in blood flow with different configurations and properties of the vascular network.