The present paper illustrates the effect of matrix cracks in longitudinal and transverse layers of cross-ply ceramic matrix composite (CMC) beams on their mechanical properties and vibration frequencies. Even in a geometrically linear problem considered in the paper, the physical non-linearity is introduced by matrix cracks and interfacial fiber-matrix friction in longitudinal layers. A closed-form solution for mechanical properties of a cross-ply CMC beam with matrix cracks is developed in the paper. The frequency of free vibrations of a simply supported beam is derived as a function of the amplitude, accounting for the effect of matrix cracks. As shown in the paper, the prediction of the natural frequencies of cross-ply CMC beams with matrix cracks in both longitudinal and transverse layers is possible using simple, yet accurate, approximate equations. © 2002 Elsevier Science Ltd. All rights reserved.