Abstract: In this paper, the dynamic stability of a viscoelastic circular cylindrical shell subject to an axial compressive force and a uniformly distributed radial compressive load is discussed. By using the replace transformation, stability conditions of viscoelastic shell under constant loads are yielded. By using synthetically the classical dynamic methods, the various dynamical properties for the dynamical system defined by the viscoelastic shell and the effect of parameters on the stability of structure are obtained.

Key words: viscoelasticity, cylindrical shell, stability