This work 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 one provides results from continuum mechanics and forms the Principles of Virtual Work and Potential Energy. Chapter two sketches the history of the FEM. Chapter three introduces the concepts of natural modes and natural stiffness. Chapter four introduces the basic concepts of the theory of composites. Chapter five applies the natural mode method to the analysis of composite beams in three dimensions. Chapter six introduces the composite plate and shell element. Chapter seven shows the computational advantages of the method on a model problem. Chapter eight deals with nonlinear analysis of anisotropic shells. Chapter nine discusses programming aspects. The volume is designed for advanced undergraduates, graduates, researchers, and practising engineers in the industry. It is accompanied by a floppy disc containing the relevant software.