The elastic behaviour of long- and short-fibre composites was described in Chapters 4 to 6. The stresses in the individual plies of a laminate under an external load and the stress distributions along short fibres were examined. This information is used to explore the ways in which a material suffers microstructural damage, leading to the ultimate failure of a component. There are two important aspects to this behaviour. Firstly, there is the deflection, degree of damage and ultimate failure of a component as a function of applied load. Secondly, there are the processes which cause absorption of energy within a composite material as it is strained. The latter determine the toughness of the material and are treated in Chapter 9. In the present chapter, attention is concentrated on predicting the applied stress at which damage and failure occur. The treatment is oriented towards long-fibre materials and laminates, and, in particular, towards polymer-based composites. Most of the principles apply equally to discontinuous reinforcement and other types of matrix. Some specific points concerning failure of such systems are dealt with in Chapter 9.