  We propose an effective geometrical approach to recover the normal form of a
given Elasticity tensor, once we know its symmetry class. In other words, we
produce a rotation which brings an Elasticity tensor onto its normal form,
given its components in any orthonormal frame, and this for any tensor of any
symmetry class. Our methodology relies on the use of specific covariants and on
the geometric characterization of each symmetry class using these covariants.
An algorithm to detect the symmetry class of an Elasticity tensor is finally
formulated.
