Abstract A general theory of damage mechanics is applied to a fibre-reinforced ceramic matrix composite, SiC/MAS-L, in order to describe its non-linear mechanical behaviour up to failure. This study is limited to the case of quasi-monotonic loading at room temperature. The model, which uses an anisotropic damage theory previously applied to other composites, is a mesoscopic-scale model which has been developed using tension–compression tests on different stacking sequences and applies in the case of multiaxial loading. It includes the marked differences observed between mechanical behaviour in tension and in compression, and is also able to predict the failure values.