Conventional cylindrical shells (made of isotropic materials) filled with or submerged in fluid have been analysed historically by using closed-form solutions or by semi-analytical method. However, these shells suffer from a serious disadvantage of not having sufficient damping, which is crucial in controlling the response of the structure during severe vibrations. One practical way of reducing response levels is by using shells with viscoelastic treatment that would result in increased damping. Previous work in this area was mostly limited to study problems whose mathematical formulation was amenable to closed-form solution or semi-analytical method. In some cases researchers resorted to experimental studies. Further, almost all previous studies were limited to lower circumferential modes and to first axial mode only. In the present paper, the method proposed overcomes most of the limitations suffered by adopting the different approaches suggested in literature. The method consists of treating fluid domain with Bessel function approach and shell domain based on first-order shear deformation theory. The present approach obviates the discretisation of liquid domain thus reducing the computation time. A computer program is developed based on the proposed method and results are compared with previous works of various researchers. A good correlation is observed for all the case studies done. Hence, it is claimed that the present approach is more universal for analysing fluid-filled or submerged shells or both. Detailed parametric studies are carried out on both conventional and viscoelastic cylindrical shells. © 2007 Elsevier Ltd. All rights reserved.