The 3D approach was employed for investigations of the global stability loss of the hollow circular cylinder made from viscoelastic composite materials. This approach is based on the investigations of the evolution of the initial infinitesimal global imperfection of the cylinder within the scope of 3D geometrically non-linear field equations of the theory of the viscoelasticity for anisotropic bodies. The numerical results of the critical forces and critical time are presented and discussed. To illustrate the importance of the results obtained using the 3D approach, these results are compared with the corresponding ones obtained by employing various approximate beam theories. The viscoelasticity properties of the cylinder material are described by the fractional-exponential operator. The numerical results and their discussion are presented for the case where the cylinder is made of an unidirectional fibrous viscoelastic composite material. In particular, it is established that the difference between the critical times obtained by employing 3D and third order refined beam theories becomes more non-negligible if the values of the external compressive force are close to the critical compressive force which is obtained at t = infinity (t denotes a time). (C) 2011 Elsevier Masson SAS. All rights reserved.