Abstract: This paper deals with methods of numerical solutions for problems of nonlinear wave propagations in arteries. Some mathematical reductions and transformation are introduced to the system of equations of nonlinear wave propagations suggested by Wu and Lee. Both the variable weighted implicit method and the SIMPLE method are used to solve the motion equations of arterial walls and the flow equations of blood, respectively. The complete results are obtained, they involve numerical solutions for propagations of the following nonlinear pulse waves:pressure, velocities and flowrate of the blood as well displacements and velocities of the arterial wall.