Cylindrical shells of arbitrary wall thickness subjected to uniform radial tensile or compressive dead-load traction are investigated. The material of the shell is assumed to be homogeneous, isotropic, compressible and hyperelastic. The stability of the finitely deformed state and small, free, radial vibrations about this state are investigated using the theory of small deformations superposed on large elastic deformations. The governing equations are solved numerically using both the multiple shooting method and the finite element method. For the finite element method the commercial program ABAQUS is used.(1) The loss of stability occurs when the motions cease to be periodic. The effects of several geometric and material properties on the stress and the deformation fields are investigated. (C) 1998 Elsevier Science Ltd. AII rights reserved.