For a better understanding of the effects of initial stress on flow in elastic tubes, the propagation of a harmonic and non-symmetrical wave in an initially stressed thick cylindrical shell filled with an inviscid fluid is studied. Although the blood is known to be a non-Newtonian fluid, for simplicity, it is assumed to be a non-viscous, while the elastic tube is considered to be isotropic and incompressible. Utilizing the theory of small deformations superimposed on large initial static deformation, for a non-symmetrical perturbed motion the governing differential equations are obtained in cylindrical polar coordinates. Due to variability of the coefficients of the resulting differential equations of the solid body, the field equations are solved by truncated power series method. Applying the boundary conditions, the dispersion relation is obtained as a function of inner pressure, axial stretch and the thickness ratio. It is observed that the wave speed of the non-symmetrical wave is large as compared to the axially symmetrical case. Various special cases are also discussed in the paper.