Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed body the axisymmetric longitudinal wave propagation in the pre-stretched compound cylinder is investigated. It is assumed that the elasticity relations of the materials of the components of the cylinder are given through the Murnagan potential. It is established that the influence of the initial stretching of the cylinders on the longitudinal wave dispersion has not only a quantitative, but also a qualitative character. The concrete numerical investigation were made for steel, tungsten (W) (as a material for the solid cylinder) and aluminium (Al) (as a material for hollow cylinder). A lot of numerical results on the wave dispersion in the compound cylinders from tungsten (W) and aluminium (Al) are presented. (C) 2004 Elsevier Ltd. All rights reserved.