We revisit here the concept of the constitutive relation error for the identification of elastic material parameters based on image correlation. An additional concept, so called constitutive compatibility of stress, is introduced defining a subspace of the classical space of statically admissible stresses. The key idea is to define stresses as compatible with the observed deformation field through the chosen class of constitutive equation. This makes possible the uncoupling of the identification of stress from the identification of the material parameters. As a result, the global cost of the identification is strongly reduced. This uncoupling also leads to parametrized solutions in cases where the solution is non-unique as demonstrated on 2D numerical examples. © 2013 Elsevier B.V.