New experimental results have made necessary the reformulation of the theory for compressive strength. The new theory is based on the precept that a number of different mechanisms can cause composite ifailure. The active one in a particular situation is that which gives the lowest failure stress. Thus composite strength can be dominated by fibre strength when the fibres are ductile, or controlled by matrix yielding when the matrix is soft. Lack of linearity in the fibres has a very important effect also, as does the adhesion between the matrix and the fibres. Modulus is affected as well as strength. Governing equations are developed for six different mechanisms and the agreement with experiment is very good. It is concluded that to make composites with good compressive properties the fibres should be hard, as straight as possible and well bonded to the matrix. The matrix should have a high yield stress, tensile strength and compressive strength. Hybridization is useful tO improve the compressive strength of Kevlar composites, but should be avoided with brittle fibre systems due to unfavourable "hybrid effects".