In this investigation, the previously proposed phenomenological model in the literature is generalized both in terms of the mathematical form of the model and the yield function used to describe the plasticity of the material. Al 1050 is chosen as the model material, where the sheets made from this material are first annealed and then subjected to a tensile test and Erichsen cupping test to obtain tensile properties as well as the FLC of the material. The constants of the generalized model are first obtained by curve fitting, whereby in this approach least overall error is expected as a single equation is used to predict the FLC of material. Further, it is shown that it would be possible to enhance the accuracy of the model at the cost of losing the applicability of a single mathematical expression for both branches of FLC. In this approach, the generalized model would be calibrated for the right branch based on Swift’s model and for the left branch based on Hill’s model. Finally, the effect of the yield criterion used to describe the plasticity of the material on the predictions of the generalized model is investigated, and it is shown that using the Hosford yield criterion yields better results compared to using the von Mises yield criterion.