Summary: We study of the stress-field generated in blood vessel walls. The analysis is based on the assumption that the compressibility of vascular walls is small but not completely ignorable. The effect of the inertial force is taken into account. Nonlinear constitutive equations suitable for the characterization of anisotropic viscoelastic behaviour of vascular tissues are used for the study. It is concluded that both compressibility and inertia have sizeable effects on the stress-field in the segments of blood vessels.