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The aim of the present paper is to investigate the effect of non-homogeneous on the stresses in composite cylinder of isotropic material subject to certain boundary conditions. The dynamical problem of an isotropic cylinder containing: (i) an isotropic core and (ii) a rigid core are considered. The elastic constants and density are taken as a power function of the radial coordinate. Analytical expressions for the component of the displacement and the components of the stresses in different cases are obtained. The numerical calculations are carried out for the component of displacement and the components of the stresses through the radial of the cylinder. The results indicate that the effect of inhomogeneity is very pronounced. Those cases have been illustrated and discussed by figures.