The analysis of well-known strength hypotheses leads to the derivation of a generalized model, which contains a number of known hypotheses as special cases and could be used for the description of the 3D-failure of hard foams. This model in the case of the strength hypothesis for hard foams is characterized by a closed surface in the principal stress space. In order to fit the model to the experimental data certain objective functions are formulated. The optimization results are shown in the Pareto-diagram (optimal solutions for several targets). The results of the fitting are plotted in the Burzyński-plane. It can be seen that reliable modeling requires the knowledge of the material behavior under hydrostatic tension and compression.