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The parameter identification of failure models for composite plies can be cumbersome, due to multiple effects as the consequence of brittle fracture. Our work proposes an iterative, nonlinear design of experiments (DoE) approach that finds the most informative experimental data to identify the parameters of the Tsai-Wu, Tsai-Hill, Hoffman, Hashin, max stress and Puck failure models. Depending on the data, the models perform differently, therefore, the parameter identification is validated by the Euclidean distance of the measured points to the closest ones on the nominal surface. The resulting errors provide a base for the ranking of the models, which helps to select the best fitting. Following the validation, the sensitivity of the best model is calculated by partial differentiation, and a theoretical surface is generated. Lastly, an iterative design of the experiments is implemented to select the optimal set of experiments from which the parameters can be identified from the least data by minimizing the fitting error. In this way, the number of experiments required for the identification of a model of a composite material can be significantly reduced. We demonstrate how the proposed method selected the most optimal experiments out of generated data. The results indicate that if the dataset contains enough information, the method is robust and accurate. If the data set lacks the necessary information, novel material tests can be proposed based on the optimal points of the parameters' sensitivity of the generated failure model surface.