This paper addresses an identification problem for a linear elastic anisotropic body. We suppose that we can measure the displacement distribution on the boundary of an elastic body induced by a known applied static load. This represents a partial knowledge of the Dirichlet to Neumann data map. From such displacement-force boundary data pairs we reconstruct the interior distribution of the elastic moduli by minimizing an error-functional based on the constitutive equation. The decomposition of this error-functional using ‘eigenelastic moduli’ and ‘eigentensors’ will indicate the limitation of identification in the anisotropic case and will be the key point in the process of minimization. Numerical results for cubic material symmetry are finally used to validate the feasibility of the proposed method.