This paper considers the multi-axial stress-strain-failure response of two commercially woven ceramic matrix composites. The different failure mechanisms of uni-axially stressed tows and woven composites are addressed. A model is postulated in which the local transverse and shear stressing, arising from the weave, instantaneously deactivate wake debonding and fiber pullout and initiates dynamic fiber failure; hence, triggering catastrophic failure of the axially stressed region of the tow. The model is shown to predict experimentally measured stress-strain-failure results for the woven composites considered. Simple stress-strain-failure models are also proposed for tows subjected to axial-transverse and axial-shear loadings, but due to the lack of experimental data they have not been validated.