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This paper presents a constrained genetic approach for reconstructing the material properties of elastic objects. The considered reconstruction problem is ill-posed and must be constrained properly so that a unique and stable numerical solution can be obtained. Qualitative prior information is incorporated using a rank-based scheme to constrain the admissible solutions. Experiments show that the proposed approach is robust when presented with noisy data and can reconstruct the elastic property accurately and reliably. In a comparison study with the deterministic Gauss-Newton methods, the constrained genetic approach also shows very consistent performance.