The solution for the matrix crack distribution in transverse layers of a cross-ply beam subjected to bending is developed based on the model of Han and Hahn (Compos Sci Technol 35 (1989) 377). This solution accounts for a bimodulus-type of the material response. As a result, it is possible to predict the extent and distribution of matrix cracks as well as the stiffness distribution in the beam subjected to bending, accounting for residual thermal stresses. The results of the solution of the bending problem are employed in the analysis of free and forced vibrations of a cross-ply beam with matrix cracks in transverse layers. The solution differs from the case of vibrations of an intact beam due to a difference in response of damaged layers under tension and compression. The results are shown for the natural frequency of a representative ceramic matrix composite (CMC) beam. © 2001 Elsevier Science Ltd. All rights reserved.