We have introduced the Mori-Tanaka theory as a new micromechanical model to predict the Young's modulus for carbon fibres, that takes into account both the crystallites and amorphous components of the carbon fibre structure. The axial elastic constants of the bulk carbon fibres were measured directly by X-ray diffraction (XRD) and an axial shear modulus of about 20 GPa was calculated. The elastic constants of the amorphous carbon in the fibres and the volume fractions of crystallites were estimated using micromechanical models. It was found that the amorphous modulus was approximately 200 GPa and the volume fractions of crystallites were 0.4 to 0.8, depending upon the nanostructure of the carbon fibres. Also, as it is known that the Raman G band shift rate per unit strain is related to the crystallite modulus, the data indicated a nearly constant value of 1.1 TPa, consistent with direct measurements upon graphene. The results show clearly that the behavior of carbon fibres can be expressed through a composite mechanical model that assumes they consist of both crystalline and amorphous carbon components.