The book presents formulations and examples of three-dimensional non-axisymmetric stability in viscoelastic anisotropic cylindrical shells. The most critical stability loss modes are determined by minimizing the critical loads and critical times with respect to the number of half-waves in radial as well as transverse directions. Currently, there is no literature available on three-dimensional local buckling analysis (or localized warpage) that considers non-axisymmetric stability loss in viscoelastic cylindrical shells. The contents of this book provide the formulation for such a stability loss analysis through the framework of the three-dimensional linearized theory of stability. Additionally, as this book addresses the problem by modeling the material as a viscoelastic fibrous composite, it can be applied to carry out buckling analysis in both elastic and viscoelastic cases. Guide to modelling composite viscoelastic shell elements for buckling analysisProvides a framework for defining the failure criterion for viscoelastic materialsCourse material for teaching shell buckling and viscoelastic composites