A methodology is proposed to optimize a specimen shape in a biaxial testing machine for the identification of constitutive laws based on full-field measurements. Within the framework of Finite Element Model Updating (FEMU) and Integrated Digital Image Correlation (IDIC), the covariance matrix of the identified material parameters due to acquisition noise is computed and its minimization is the basis of the proposed shape optimization. Two models are investigated; first, a linear elastic law, and second, an elastoplastic law with linear kinematic hardening. Two optimal fillet radii sets are assessed for the two investigated laws based on the minimization of the identification uncertainty.