In order to understand the mechanical behaviours of ceramic matrix composites under various loading conditions, the compression stress-strain behaviour of a cross woven C/SiC ceramic matrix composite was characterized in terms of damage and fracture mechanisms, which were observed by scanning electron microscope (SEM) on a side-polished sample. The compression stress-strain curve was found to consist of two stages. The first stage, which extends to about 300 MPa, covers linear elastic deformation with a compression modulus of 140 GPa. The second stage starts with the occurrence of compression damage modes, which include ply delamination, bundle separation and transverse bundle cracking. Depending on the local structure of the sample, the second stage of the stress-strain curve can be either mostly linear or non-linear. The fracture of the composite under compression is by kinking, shearing and bending fracture of fibre bundles individually or in groups, forming a macroscopic shear band in the sample.