Abstract: The guided wave characteristics of multilayered hollow cylinders with initial stresses in the axial and radial directions were investigated based on the principles of the mechanics of incremental deformations. The Legendre polynomial series method was used to solve the coupled wave equations. The convergence of the polynomial method is discussed alongside the numerical example in the paper. The influences of initial stresses on longitudinal waves and on torsional waves, respectively, were investigated. Numerical results show that the influences of the initial stresses on longitudinal waves and on torsional waves are quite distinct. Moreover, the influences of initial axial stress on dispersion curves are very different from those of initial radial stress.