Abstract: This paper studied the elementary waves for the blood flow in veins. The blood flow in veins could be described by a 3 × 3 nonlinear partial differential equations. It was a non strict hyperbolic system. Using the characteristic analysis method, the elementary waves, including rarefaction wave, shock wave, and stationary wave, were obtained constructively. In particular, for stationary wave in blood flow in veins, it was proved that there existed a region Ω in the phase space where stationary wave could be connected by a state when the given state was outside the region

Key words: blood flow in veins, elementary waves, stationary wave, nonstrict hyperbolic system