This book is the first to focus on mechanical aspects of fibrous and layered composite materials with curved structure. By mechanical aspects it is meant that the reinforcing layers or fibres have some initial curvature, bending or distortion which may occur as a result of design, or as a consequence of some technological process. The new, accurate techniques were developed in the framework of continuum theories for piecewise homogeneous bodies. Linear and non-linear problems in the framework of this continuum theory as well as in the framework of the piecewise homogeneous body model are considered. It is assumed that the reader is familiar with the theory of elasticity for anisotropic bodies, with partial differential equations and integral transformations, and also with the FEM. This book is designed for graduate researchers, for mechanical engineers designing composite materials for automobiles, trucks, flywheels etc., and for civil, aerospace, and biomedical engineers.