For the determination of material parameters, it is a common practice to extract specimens with well-defined geometries. The design of the samples and the choice of the applied load are meant to lead to a homogeneous stress and strain distribution in a part of the sample. When applied to biological materials, this raises a number of problems: homogeneous strains cannot be obtained because the materials have inhomogeneous properties, and the manufacturing of samples is hard or sometimes impossible. In this technical note a different approach is presented, based on the use of a digital image technique for the measurement of nonhomogeneous strain distributions, finite element modeling and the use of a minimum-variance estimator. The method is tested by means of experiments on an orthotropic elastic membrane of a woven and calendered textile. Five parameters are identified using the experimental data of one single experiment.