A theory to predict the ultimate tensile strength of fibre-reinforced ceramics (CMCs) is presented. The theory incorporates the statistical nature of the fibre strength and the presence of fibre/matrix sliding, the latter allowing broken fibres to retain some load-carrying capacity, and yields a simple analytic expression for the strength. Comparisons with measurements on a wide range of CMCs indicate that the theory improves considerably on rule-of-mixtures estimates. An extension of the concepts used for CMCs to metal-matrix composites (MMCs) with weak, sliding fibre/matrix interfaces is then proposed, and the resultant predictions for MMC strengths agree well with data on SCS-6/Ti-alloy materials.