The paper presents an approach to the analysis of axisymmetric vibrations of thick-walled specially orthotropic multilayered cylindrical tubes. The first part of the paper is concerned with the case where thermal residual stresses are negligible. The effect of these stresses on vibrations is considered in the second part using governing equations in variations, i.e. a superposition of a dynamic solution on preexisting static deformations. Equations of radial and axial vibrations of specially orthotropic tubes can be uncoupled, but coupling is present in the boundary and continuity conditions. It is shown that thermal residual stresses affect both axial and radial vibrations.