In this study, the propagation of time harmonic waves in prestressed, anisotropic elastic tubes filled with viscous fluid is studied. The fluid is assumed to be incompressible and Newtonian. A two layered hyperelastic anisotropic structural model is used for the compliant arterial wall. The tube is subjected to a static inner pressure P(i) and an axial stretch lambda. The governing differential equations of tube are obtained in cylindrical coordinates, utilizing the theory of "Superposing small deformations on large initial static deformations". The analytical solutions of the equations of motion for the fluid have been obtained. Due to variability of the coefficients of the resulting equations for the solid body they are solved numerically. The dispersion relation is obtained as a function of the stretch and material parameters. (C) 2011 Elsevier Inc. All rights reserved.