The commonly accepted production methods of composite systems generally result in departure of the plies properties from transverse isotropy due to stresses acting during fibre-matrix bond formation. This anisotropy coupled with the composite structure affects compressive loading; the ultimate stresses as well as the direction, in- or out-of-plane, of kink propagation. A unidirectional and a crossply carbon fibre/PEEK composites were compression tested at ambient and elevated temperature as well as exposed to various chemical environments. Significant disruptions in fibre-matrix interface in the crossply composite were indicated. The compression tests showed that failure occurred through in-plane and out-of-plane fibre bucking and kinking in the unidirectional and crossply composites, respectively. Failure of the longitudinal plies in the crossply laminate occurred at significantly higher compression stress than for the unidirectional composite. Compressive failure mechanisms in unidirectional and multi-directional laminates are considered.