A folly nonlinear model of arterial blood flow and pressure pulse propagation which can account for tapering, branching, variable thickness and nonlinear elastic properties of the arterial wall is presented. The model can accommodate different elastic modulus for Collagen and Elastin fibbers, with a recruitment function for the former. One dimensional momentum and continuity equations coupled with a pressure-area relationship yields a system of nonlinear hyperbolic partial differential equations. The system is reduced to the canonic form and solved by a "Hartree" like Finite Difference Method over the characteristics. A complete model of the human arterial system is implemented, giving geometrical and physical data for the major vessels and, appropriate inlet and outlet boundary conditions, using a windkessel approximation for peripheral vascular resistance and compliance. An experiment of vasodilatation and vasoconstriction is simulated, exhibiting features of the natural pulses along the arm's arteries and comparison is made with clinical data reported in the literature . Resulting pressure and diameter waves, show similar changes to those that occurs in aging and moderate hypertension.