With consideration of a full set of mechanical properties: elasticity, viscosity, and axial and circumferential initial tensions, and radial and axial motion of the arterial wall, this paper presents a theoretical study of pulse wave propagation in arteries and evaluates pulse wave velocity and transmission at the carotid artery (CA) and the ascending aorta (AA). The arterial wall is treated as an initially-tensioned, isotropic, thin-walled membrane, and the flowing blood in the artery is treated as an incompressible Newtonian fluid. Pulse wave propagation in arteries is formulated as a combination of the governing equations of radial and axial motion of the arterial wall, the governing equations of flowing blood in the artery, and the interface conditions that relate the arterial wall variables to the flowing blood variables. We conduct a free wave propagation analysis of the problem and derive a frequency equation. The solution to the frequency equation indicates two waves: Young wave and Lamb wave, propagating in the arterial tree. With the related values at the CA and the AA, we evaluate the influence of arterial wall properties on their wave velocity and transmission, and find the opposite effects of axial and circumferential initial tensions on transmission of both waves. Physiological implications of such influence are discussed.