Nano-indentation instrumented tests are carried out at shallow depths on PAN-based and MPP-based carbon fibres. Indentation moduli are obtained by performing the tests at ten different measured orientations with respect to the fibre axis. They are used to identify the elastic constants of the fibres, assuming a transversely isotropic behaviour, by minimising a cost function between measured and estimated values. Inconstancies between the identified in-plane shear and transverse moduli and reported literature values are pointed out, and some drawbacks of the nano-indentation method are highlighted. An improved method taking into account the buckling mechanisms of crystallites at stake during the indentation process, and visible in the hysteretic behaviour of force-penetration nanoindentation curves, is proposed. It allows to identify values of elastic constants that are in accordance with literature values. These elastic properties of carbon fibres are in turn used to estimate the elastic properties of epoxy matrix composites containing these fibres. Very good agreement is found with experimentally available values of unidirectional ply properties. An excellent correlation between experiments and Finite Element Analyses of the indentation response of carbon fibres is eventually found.