Shell structures are key components in a very wide range of engineering enterprises. The theory of layered shells of revolution under the quasistatic action of loading and temperature is the subject of this book. The shells treated here are in general of an asymmetric sandwich structure. A linear theory is developed which allows for a transition to shells with less layers, that is two-layered and homogeneous structures.The first half of the book is concerned with orthotropic elastic shells. In particular, it includes the membrane theory of cylindrical, spherical and conical shells, and the bending theory of cylindrical shells, storage tanks and pressure-vessels. In each of the numerical examples considered, an attempt is made to map different regimes of structural behaviour.The second half of the book is devoted to viscoelastic shells. First the time-invariant hereditary theory is presented, describing the response of viscoelastic materials. According to the correspondence principle of this theory the actual viscoelastic shell may be replaced by a conjugate elastic one. In this way many of the results from the first half of the book can be put to good use even for viscoelastic shells. The time-dependent material characteristics are taken into account by means of the time-temperature principle.In an appendix (Part VI), the mathematical prerequisites are presented. With viscoelasticity comes the need to employ further mathematical disciplines; integral equations and integral transformations are usually encountered. Here, instead, a different concept has been chosen, the distributional concept of Laurent Schwartz, which allows many problems to be tackled in a simple formal way. In discussing the distribution theory, a level accessible to a technical reader has been maintained.The book is intended as a textbook for students and teachers of structural and aeronautical engineering. The book will also appeal to a broad range of practising engineers working in areas of aeronautical, civil, and mechanical engineering, as well as to those working for firms dealing with shell structures.