Employing the theory of small deformations superimposed on large initial static deformations, the propagations of harmonic waves in an initially stressed thick elastic tube filled with a viscous fluid is studied. Due to variability of the coefficients of the resulting differential equation of the tube, the field equations are solved by a power series method. Utilizing the properly posed boundary conditions that characterize the reaction of fluid with the tube wall, the dispersion relation is obtained as a function of initial deformations and the geometrical characteristics. The dispersion equation is examined analytically, whenever it is possible, and numerically, and the results are depicted on some graphs. It is observed that wave speeds increase with thickness parameter.