Summary: A continuum damage mechanics constitutive model is developed to describe the mechanical behavior of fiber-reinforced ceramic matrix composites submitted to complex multiaxial loadings. This model relies on the use of a phenomenological internal damage variable defined as the change of the compliance tensor induced by any given loading. Microstructural observations of the damage entities provide qualitative data allowing us to formulate physically founded simplifying hypotheses. The evolution laws of scalar damage variables derived from the components of the compliance tensor are established within a classical thermodynamic framework, using coupled multicriteria expressed in the space of the associated thermodynamic forces. Damage deactivation processes related to the unilateral crack closure effect observed under compressive loadings are introduced through the definition of effective compliance tensor components. This approach is applied to a 2-D woven SiC/SiC composite processed by chemical vapor infiltration (CVI). Major advantages and drawbacks of the proposed approach as observed from various validation tests are discussed.