An analysis of the onset of wrinkling is first developed for a doubly curved, elastic-plastic shell element submitted to a biaxial plane stress loading. Plastic yielding is described using a criterion recently proposed for anisotropic sheet metals. The wrinkling limit curves obtained with this analysis are compared with previous results based on different yield criteria. Finite element (FE) simulations of a deep-drawing experiment are also performed using the Abaqus/Explicit code with the aim of comparing the FE results relating to the initiation of wrinkling with the predictions of the analytical model and with experiments from the literature.