By the use of the Murnaghan potential the influence of third order elastic constants on axisymmetric longitudinal wave propagation velocity in a pre-stressed two-layered circular hollow cylinder is investigated. This investigation is carried out within the scope of the piecewise homogeneous body model by utilizing the first version of the small initial deformation theory of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies. Numerical results are obtained and analyzed for the cases where the material of the outer hollow cylinder material is aluminum, but the material of the inner cylinder is steel (Case 1) and tungsten (Case 2). These results are obtained not only for the case where the initial uniaxial stress is a stretching one, but also for the case where the initial uniaxial stress is a compressing one. According to these results, it is established that the third order elastic constants of the selected materials influence not only quantitatively, but also qualitatively the axisymmetric wave propagation velocity in the initially stressed two-layered hollow cylinder. It is also established that the mentioned influence in Case 2 is more significant than that in Case 1.