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Quantitative measurement of the material properties (eg, stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness, and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full-field displacement data—ie, we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest—and seek stiffness parameters that lead to balanced internal and external forces in a model. For in vivo applications, the displacement data can be acquired clinically using magnetic resonance imaging while the forces may be computed from pressure measurements, eg, through catheterization. We outline a set of conditions under which the least-square force error objective function is convex, yielding uniquely identified material properties. An important component of our framework is a new numerical strategy to formulate polyconvex material energy laws that are linear in the material properties and provide one optimal description of the available experimental data. An outcome of our approach is the analysis of the reliability of the identified material properties, even for material laws that do not admit unique property identification. Lastly, we evaluate our approach using passive myocardium experimental data at the material point and show its application to identifying myocardial stiffness with an in silico experiment modeling the passive filling of the left ventricle. Copyright © 2017 John Wiley & Sons, Ltd.