We have used the Mori-Tanaka theory to develop a new micromechanical model to predict the Young's modulus for carbon fibres, taking into account both the crystallites and amorphous components of the fibre structure. In order to follow the dependence of the mechanical properties of the fibres upon nanostructure, we prepared five different types of PAN-based fibres, with Young's moduli in the range 200-500 GPa. The axial elastic constants of the bulk carbon fibres were measured directly by X-ray diffraction 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. It was found that the amorphous modulus was approximately 200 GPa and the volume fractions of crystallites were 0.4-0.8, 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. 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.