The effect of matrix microcracking on the stiffnesses of a carbon-fibre/SiC-matrix woven composite is studied by means of an ultrasonic method. it provides the whole set of the stiffness tensor coefficients which are inaccessible by classical strain measurements and which are required to identify anisotropic damage. The induced anisotropy depends on the loading direction. If a tensile solicitation in a fibre direction leads to stiffnesses decreases without any rotation of principal axes, a tensile solicitation of 45 degrees from a fibre direction creates microcracks with a predominant orientation that does not coincide with the elastic symmetry axes, and induce a fully anisotropic elastic degradation.