Over past decades, wave propagation within the arterial vasculature has attracted much attention. This can be attributed to the interest in understanding how blood flow and pressure waveforms change with aging and hypertension. To properly understand cardiovascular dynamics associated with these changes, all aspects of the system must be considered including the fluid dynamics, the impact of the arterial wall, and the upstream and downstream vasculature. A mathematical model of the aforementioned quantities allows for prediction of pressure and flow waveforms. The biomechanical properties of the vessels change along the axial direction as well as with aging or hypertension. As vessels decrease in size, they become stiffer, an effect that is amplified by the aging process. The stiffening of vessels affects not only the wave propagation speed but also the shape profile of pressure waves as they travel along the vessels. Mathematical modeling can provide an essential tool for investigating how changes in wall properties and outflow boundary conditions impact wave propagation. These models can eventually be rendered into a patient-specific model to demonstrate the changing effects on an individual. This study uses a one-dimensional fluid dynamics model coupled with a viscoelastic wall model that can predict volumetric blood flow, pressure, and vessel area waveforms in arterial networks. The fluid dynamics model is derived from the Navier-Stokes equations for an incompressible fluid in a cylinder, and the wall model is derived from nonlinear elasticity theory relating pressure and vessel area. A number of wall models are investigated combining linear and nonlinear elastic responses in geometries with and without vessel tapering. We further investigate how the impact of comparing downstream vasculature is represented by a three-element Windkessel model composed of two resistors and a capacitor whose values are found through comparing the impedance spectrum with that of a structured tree model with a structured tree model in which we solve a wave equation. Varying the parameters in both the wall model and the boundary model allows us to regulate the stiffness along each vessel as well as the upstream effects caused by the downstream vasculature. This study used the one-dimensional model to simulate flow, pressure, and area waveforms in a large network geometry representing the pulmonary vasculature in healthy and hypertensive subjects calibrated to data from mouse and human studies.