Axial compression fracture of carbon fibres was studied by embedding single fibres in epoxy resin and compressing the specimens parallel to the fibre axis. By careful optical monitoring of the fibre surface the earliest stages of fracture were identified leading to estimates of the fibre axial compression failure strengths. Compression strength decreases markedly from about 2.2 GN m−2 for moderately oriented fibres to <1 GN m−2 for highest modulus filaments. The trend towards decreasing compression strength with increasing anisotropy is explained on the basis of an increasing fibre microfibrillar nature. However fracture morphology studies show that the unduly rapid strength decrease results from an increasing degree of fibre outer layer ordering which accompanies increasing axial anisotropy in carbon fibres since cracking occurs first on the more highly aligned filament surfaces. It is suggested that fibre compression fracture changes from a shear to a microbuckling or kinking mode with increasing fibre anisotropy, where the latter initiates in individual, well-aligned but uncoupled microfibrils. The similarity of fine axial compression fractures in oriented carbon fibres to those found in elastica loop experiments is noted as are the possible implications which the low strain-to-failure in compression of very high modulus fibres might have for practical composites.