This work deals with the problem of characterising the elastic properties of a composite material at both me- soscopic (ply-level) and microscopic (constitutive phases-level) scales. This goal is attained by means of an adequate multi-scale identification strategy (MSIS) which aims at identifying the constitutive properties, at each relevant scale, by exploiting the information restrained in the macroscopic dynamic response of the composite. In this background, the multi-scale identification problem is split into two interdependent sub-problems which are stated, at both levels, as constrained minimisation problems. At the first level the goal is the characterisation of the lamina properties by minimising the distance between the numerical and the reference harmonic re- sponses of the composite. The second level problem aims at identifying the elastic properties of both fibre and matrix by minimising the distance between the effective elastic properties evaluated through a homogenisation process and those provided by the first-level inverse problem. The MSIS is based on a special global hybrid optimisation tool and on the strain energy homogenisation method of periodic media. Its effectiveness is proven through a meaningful benchmark.