Superplasticity is the ability of polycrystalline materials under certain conditions to exhibit extreme tensile elongation in a nearly homogeneous/isotropic manner. Historically, this phenomenon was discovered and systematically studied by metallurgists and physicists. They, along with practising engineers, used materials in the superplastic state for materials forming applications. Metallurgists concluded that they had the necessary information on superplasticity and so theoretical studies focussed mostly on understanding the physical and metallurgi- cal properties of superplastic materials. Practical applications, in contrast, were led by empirical approaches, rules of thumb and creative design. It has become clear that mathematical models of superplastic deformation as well as analyses for metal working processes that exploit the superplastic state are not adequate. A systematic approach based on the methods of mechanics of solids is likely to prove useful in improving the situation. The present book aims at the following. 1. Outline briefly the techniques of mechanics of solids, particularly as it applies to strain rate sensitive materials. 2. Assess the present level of investigations on the mechanical behaviour of superplastics. 3. Formulate the main issues and challenges in mechanics ofsuperplasticity. 4. Analyse the mathematical models/constitutive equations for superplastic flow from the viewpoint of mechanics. 5. Review the models of superplastic metal working processes. 6. Indicate with examples new results that may be obtained using the methods of mechanics of solids.