Employing the theory of small deformations superimposed on large initial static deformation, the propagation of harmonic waves in a prestressed viscoelastic tube (artery) filled with a viscous fluid (blood) is studied. Due to variability of the coefficients of the resulting differential equations of the solid body, the field equations are solved by a power series method. Using the properly posed boundary condtions, the dispersion relation is obtained as a function of initial deformations and geometrical characteristics. The numerical results indicate that the viscoelastic character of the tube material effects the dispersion relation considerably. It is observed that at high frequencies the viscosity of the fluid becomes quite important.