A volume integral equation method is used to investigate the mechanics of damage evolution in a unidirectional SiC/Ti composite under transverse loading. It is shown that the most likely mechanism of the damage is the initiation of partial ®ber debonding followed by transverse cracking (in brittle matrix composites, e.g., SiC/Ti 3 Al) or plastic yielding (in ductile matrix composites, e.g., SiC/Ti-15-3). The matrix damage has been observed to occur at extremely low transverse loads and a rational explanation of this phenomenon does not appear to have been given previously in the literature. Our results indicate that the initiation of matrix cracking or yielding can be explained if microcracks are present in the ®ber-matrix interface zone. In absence of the microcracks the stresses in the matrix are too low to cause any damage.