In the previous two chapters, some background was given about the various types of reinforcement and the ways in which they may be distributed within different matrices. In this chapter, attention is turned to the problem of predicting the behaviour of the resulting composites. Prime concern is with the mechanical properties. The incorporation of the reinforcement is usually aimed at enhancing the stiffness and strength of the matrix. The details of this enhancement can be rather complex and difficult to describe with complete rigour. The simplest starting point is to consider the elastic behaviour of a composite with continuous fibres, all aligned in the same direction. Aligned composites are normally used to exploit the stiffness (and strength) parallel to the fibres. However, it is also important to understand the way they behave when loaded in other directions. The treatment therefore includes the behaviour under transverse loading. In this chapter and in the following one, the assumption is made that there is perfect bonding between fibre and matrix across the interface between them. The detailed nature of the interfacial region, and the consequences of imperfect bonding, are considered in Chapter 7.