A rational methodology is developed for optimal design of biaxial stretch tests intended for estimating material parameters of flat tissues. It is applied to a structural model with a variety of constitutive equations and test protocols, and for a wide range of parameter levels. The results show nearly identical optimal designs under all circumstances. Optimality is obtained with two uniaxial stretch tests at mutually normal directions inclined by 22.5 deg to the axes of material symmetry. Protocols which include additional equibiaxial tests provide superior estimation with lower variance of estimates. Tests performed at angles 0, 45, and 90 deg to the axes of material symmetry provide unreliable estimates. The optimal sampling is variable and depends on the protocols and model parameters. In conclusion, the results indicate that biaxial tests can be improved over presently common procedures and show that this conclusion applies for a variety of circumstances.