This book is a foray into the computer analysis of three-dimensional composite structures using the finite element method (FEM).The text advances from the analysis of simple beams to arbitrary anisotropic and composite plates and shells; it treats both linear and nonlinear behaviour. Once the basic philosophy of the method is understood, the reader may expand its application and modify the computer programs to suit particular needs. It is shown how this leads to considerable savings in computer time. Chapter 1 provides results from continuum mechanics and forms the Principles of Virtual Work and Potential Energy. Chapter 2 sketches the history of the FEM. Chapter 3 introduces the concepts of natural modes and natural stiffness. Chapter 4 introduces the basic concepts of the theory of composites. Chapter 5 applies the natural mode method to the analysis of composite beams in three dimensions. Chapter 6 introduces the composite plate and shell element. Chapter 7 shows the computational advantages of the method on a model problem. Chapter 8 deals with nonlinear analysis of anisotropic shells. Chapter 9 discusses programming aspects. The volume is designed for advanced undergraduates, graduates, researchers, and practising engineers in the industry. The book is accompanied by a floppy disc containing the relevant software.