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