The problem of initial damage in angle-ply [-m/0n/m]and [-/]ceramic matrix composites subjected to axial tension is considered in this paper. The damage is in the form of matrix cracks that may appear in either inclined (- and lamination angle)or longitudinal layers. As follows from the analysis, if the lamination angle of the inclined layers is small, the initial failure occurs in the 0-layers of [-m/0n/m]composites or in [-/]composites in the form of bridging cracks. However, if the inclined layers form a larger angle with the load direction, they fail due to tunneling cracks. It is shown that the boundary between two different modes of failure in a representative SiC/CAS composite corresponds to a lamination angle equal to 35° in the case of [-m/0n/m]composites. In the case of [-/]laminates, the boundary value of the lamination angle is equal to 45°, i.e. bridging cracks form if <45° and tunneling cracks appear if >45°